Loading [MathJax]/jax/element/mml/optable/GeneralPunctuation.js
Research article Special Issues

Research on cost accounting of enterprise carbon emission (in China)

  • Received: 04 July 2022 Revised: 01 August 2022 Accepted: 04 August 2022 Published: 15 August 2022
  • Enterprises in China face two major challenges about their existence and energy supply at present. One is the difficulty in providing enough energy at an acceptable and reasonable price; the other is a severe environmental issue caused by over-consumption of energy. The government and relevant enterprises, therefore, mainly focus on carbon emission reduction, and the cost accounting of carbon emission, an essential prerequisite, and object of carbon emission reduction, should be further attention. The carbon emission cost is divided into internal cost and external cost, combined with the extended accounting model and cost calculation. This can comprehensively measure and reflect the two costs of the life cycle of the product, provide more relevant data and information support for the deepening and development of the circular economy, and provide an effective cost information basis and guide enterprise managers for scientific decision-making and governance.

    Citation: Hexiao Hu, Yalian Zhang, Chen Yao, Xin Guo, Zhijing Yang. Research on cost accounting of enterprise carbon emission (in China)[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11675-11692. doi: 10.3934/mbe.2022543

    Related Papers:

    [1] Tariq Al-Hawary, Ala Amourah, Abdullah Alsoboh, Osama Ogilat, Irianto Harny, Maslina Darus . Applications of qUltraspherical polynomials to bi-univalent functions defined by qSaigo's fractional integral operators. AIMS Mathematics, 2024, 9(7): 17063-17075. doi: 10.3934/math.2024828
    [2] Sheza. M. El-Deeb, Gangadharan Murugusundaramoorthy, Kaliyappan Vijaya, Alhanouf Alburaikan . Certain class of bi-univalent functions defined by quantum calculus operator associated with Faber polynomial. AIMS Mathematics, 2022, 7(2): 2989-3005. doi: 10.3934/math.2022165
    [3] Ala Amourah, B. A. Frasin, G. Murugusundaramoorthy, Tariq Al-Hawary . Bi-Bazilevič functions of order ϑ+iδ associated with (p,q) Lucas polynomials. AIMS Mathematics, 2021, 6(5): 4296-4305. doi: 10.3934/math.2021254
    [4] Luminiţa-Ioana Cotîrlǎ . New classes of analytic and bi-univalent functions. AIMS Mathematics, 2021, 6(10): 10642-10651. doi: 10.3934/math.2021618
    [5] Jianhua Gong, Muhammad Ghaffar Khan, Hala Alaqad, Bilal Khan . Sharp inequalities for q-starlike functions associated with differential subordination and q-calculus. AIMS Mathematics, 2024, 9(10): 28421-28446. doi: 10.3934/math.20241379
    [6] Pinhong Long, Jinlin Liu, Murugusundaramoorthy Gangadharan, Wenshuai Wang . Certain subclass of analytic functions based on q-derivative operator associated with the generalized Pascal snail and its applications. AIMS Mathematics, 2022, 7(7): 13423-13441. doi: 10.3934/math.2022742
    [7] Pinhong Long, Xing Li, Gangadharan Murugusundaramoorthy, Wenshuai Wang . The Fekete-Szegö type inequalities for certain subclasses analytic functions associated with petal shaped region. AIMS Mathematics, 2021, 6(6): 6087-6106. doi: 10.3934/math.2021357
    [8] Shuhai Li, Lina Ma, Huo Tang . Meromorphic harmonic univalent functions related with generalized (p, q)-post quantum calculus operators. AIMS Mathematics, 2021, 6(1): 223-234. doi: 10.3934/math.2021015
    [9] Saqib Hussain, Shahid Khan, Muhammad Asad Zaighum, Maslina Darus . Certain subclass of analytic functions related with conic domains and associated with Salagean q-differential operator. AIMS Mathematics, 2017, 2(4): 622-634. doi: 10.3934/Math.2017.4.622
    [10] Huo Tang, Kadhavoor Ragavan Karthikeyan, Gangadharan Murugusundaramoorthy . Certain subclass of analytic functions with respect to symmetric points associated with conic region. AIMS Mathematics, 2021, 6(11): 12863-12877. doi: 10.3934/math.2021742
  • Enterprises in China face two major challenges about their existence and energy supply at present. One is the difficulty in providing enough energy at an acceptable and reasonable price; the other is a severe environmental issue caused by over-consumption of energy. The government and relevant enterprises, therefore, mainly focus on carbon emission reduction, and the cost accounting of carbon emission, an essential prerequisite, and object of carbon emission reduction, should be further attention. The carbon emission cost is divided into internal cost and external cost, combined with the extended accounting model and cost calculation. This can comprehensively measure and reflect the two costs of the life cycle of the product, provide more relevant data and information support for the deepening and development of the circular economy, and provide an effective cost information basis and guide enterprise managers for scientific decision-making and governance.



    Notation: For two sequences of positive constants {an,n1} and {bn,n1}, symbols anbn, an=O(bn) and an=o(bn) stand for liman/bn=1, liman/bn(0,) and liman/bn=0, respectively. For simplicity, we shall write P, a.s. and Lp to express the convergence in probability, the almost certain convergence and p-mean convergence, respectively.

    The following concept of superadditive function was introduced in [1].

    Definition 1.1. A function ϕ:RnR is called superadditive if ϕ(xy)+ϕ(xy)ϕ(x)+ϕ(y) for all x,yRn, where is for componentwise maximum and is for componentwise minimum.

    Hu [2] introduced the concept of negatively superadditive-dependent (NSD) based on the above concept of superadditive function.

    Definition 1.2. A random vector X=(X1,X2,,Xn) is said to be NSD if

    Eϕ(X1,X2,,Xn)Eϕ(X1,X2,,Xn),

    where X1,X2,,Xn are independent such that Xi and Xi have the same distribution for each i and ϕ is a superadditive function such that the expectations in the above equation exists. A sequence {Xn,n1} of random variables is said to be NSD if for each n1, (X1,X2,,Xn) is NSD.

    Hu [2] established some basic properties and three structural theorems of NSD random variables. An interesting example was also presented in [2], which illustrated that NSD is not necessarily negatively associated (NA, [3]). Christofides and Vaggelatou [4] showed that NA is NSD. Eghbal et al. [5] derived two maximal inequalities and strong law of large numbers of quadratic forms of NSD random variables. Shen et al. [6] studied almost sure convergence and strong stability for weighted sums of NSD random variables. Wang et al. [7] studied complete convergence for arrays of rowwise NSD random variables, with applications to nonparametric regression. For more research of the limit theory for NSD random variables, the author can refer the reader to [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24].

    NA random variable has been studied many times and attracted extensive attention, so it is very significant to investigate the limit theorems of this wider NSD class, which is highly desirable and of considerable significance in theory and application.

    A random variable X is called to be a two-tailed Pareto distribution whose density is

    f(x)={qx2ifx1,0if1<x<1,px2ifx1, (1.1)

    where p+q=1.

    Let {Xn,n1} be independent Pareto-Zipf random variables satisfying P(Xn=0)=11/n,

    P(Xnx)=11x+nforallx>0, (1.2)

    and fXn(x)=1(x+n)2I(x>0).

    Obviously, if the random variable Xn satisfies Eq (1.1) or (1.2), then E|Xn|=, n1. Alder [25] considered independent and identically distributed (i.i.d.) random variables satisfying Eq (1.1) and studied the strong law of large numbers. Alder [26] obtained the weak law of large numbers for Pareto-Zipf random variables. For more research on laws of large numbers for i.i.d. random variables with infinite mean, the author can refer to works of Adler [27,28] and Matsumoto and Nakata [29,30,31].

    Yang et al. [24] investigated the law of large numbers for NSD random variables satisfying Pareto-type distributions with infinite means, and obtained the following theorems which extend and improve the corresponding ones in [25,26]:

    Theorem 1.1. Let {Xn,n1} be a nonnegative sequence of NSD random variables whose distributions are defined by P(Xn=0)=11/cn for n1 and the tail probability

    P(Xn>x)=1x+cnforallx>0andn1, (1.3)

    where {cn} is a nondecreasing constant sequence with cn1 and

    Cn=nj=11cj. (1.4)

    Then we have

    nj=1c1jXjCnlogCnP1. (1.5)

    Theorem 1.2. Let {Xn,n1} be a sequence of NSD random variables with the same distributions from a two-tailed Pareto distribution defined by Eq (1.1). Then for all β>0 we have

    1logβnnj=1logβ2jjXja.s.pqβ. (1.6)

    In the current work, the author studies the weak and strong laws of large numbers for NSD random variables. The obtained results in this article extend and improve Theorems 1.1 and 1.2. Meanwhile, the author investigates p-mean convergence for NSD random variables under some appropriate conditions, which was not considered in [24].

    Throughout this paper, the symbol C denotes a positive constant which may differ from one place to another. The symbol I(A) denotes the indicator function of the event A.

    To prove our main results, we first present some technical lemmas.

    Lemma 2.1. ([2]) If (X1,X2,,Xn) is NSD and f1,f2,,fn are all non decreasing, then (f1(X1),f2(X2),,fn(Xn)) is also NSD.

    As we know, moment inequalities are very important tools in establishing the limit theorems for sequences of random variables. Shen et al. [6] presented the following Marcinkiewicz-Zygmund inequality with exponent 2.

    Lemma 2.2. ([6]) Let {Xn,n1} be a sequence of NSD random variables with EXn=0 and EX2n< for n1. Then

    E(max1kn(ki=1Xi)2)2ni=1EX2i,n1.

    By means of similar methods in Shao [32], Wang et al. [7] established the following Rosenthal-type maximal inequality, which is very useful in establishing the convergence properties for NSD random variables:

    Lemma 2.3. ([7]) Let p>1. Let {Xn,n1} be a sequence of NSD random variables with E|Xi|p< for each i1. Then for all n1,

    E(max1kn|ki=1Xi|p)23pni=1E|Xi|pfor1<p2

    and

    E(max1kn|ki=1Xi|p)2(15plnp)p[ni=1E|Xi|p+(EX2i)p/2]forp>2.

    Lemma 2.4. ([6]) Let {Xn,n1} be a sequence of NSD random variables. If

    n=1Var(Xn)<,

    then n=1(XnEXn) almost certainly converges.

    Now we state our main results and the proofs will be presented in next section.

    Theorem 2.1. Let {Xn,n1} be a nonnegative sequence of NSD random variables whose distributions are defined by P(Xn=0)=11/cn for n1 and the tail probability

    P(Xn>x)=1x+cnforallx>0andn1, (2.1)

    where {cn,n1} is a nondecreasing constant sequence with cn1 and

    Cn=nj=11cj. (2.2)

    Let {Dn,n1} be a sequence of constants satisfying Dn and Cn=o(Dn). Then we have

    1Dnmax1kn|kj=1c1j(XjEXnj)|P0, (2.3)

    where Xnj=XjI(XjDncj)+DncjI(Xj>Dncj), 1jn.

    Take Dn=CnlogCn, then we can obtain the following corollary which extends Theorem 1.1.

    Corollary 2.1. Let {Xn,n1} be a nonnegative sequence of NSD random variables whose distributions are defined by P(Xn=0)=11/cn for n1 and the tail probability Eq (2.1), where {cn,n1} is a nondecreasing constant sequence satisfying cn1 and Eq (2.2). Then

    1CnlogCnmax1kn|kj=1c1j(XjEXnj)|P0. (2.4)

    Remark 2.1. Yang et al. [24] proved that

    1CnlogCnnj=1c1jEXjI(XjcjCnlogCn)1

    and

    1CnlogCnnj=1c1jE(cjCnlogCnI(Xj>cjCnlogCn))=nj=1P(Xj>cjCnlogCn)0,

    which yields

    1CnlogCnnj=1c1jEXnj1.

    Then we can find that Theorem 1.1 is a special case of Corollary 2.1 for k=n. Therefore, Theorem 2.1 and Corollary 2.1 extend and improve Theorem 1.1.

    Theorem 2.2. Let {Xn,n1} be a sequence of identically distributed NSD random variables. Let {dn,n1} be a sequence of positive constants satisfying dn, and {cn,n1} be a sequence of positive constants such that φ(n)cndn satisfies φ(n) as n,

    m=n1φ2(m)=O(nφ2(n)) (2.5)

    and

    n=1P(|X1|>φ(n))<. (2.6)

    Then

    1dnnj=1c1j(XjE~Xj)0a.s., (2.7)

    where ~Xj=φ(j)I(Xj<φ(j))+XjI(|Xj|φ(j))+φ(j)I(Xj>φ(j)), 1jn.

    Remark 2.2. We will show that Theorem 1.2 is a special case of Theorem 2.2. In fact, if we assume that {Xn,n1} is a sequence of NSD random variables with the same distributions from a two-tailed Pareto distribution defined by Eq (1.1), and take cn=nlog2βn and dn=logβn (β>0), then φ(n)=cndn=nlog2n. We can verify that φ(n)=nlog2n satisfies the conditions stated in Theorem 2.2.

    First, it is clear that φ(n)=nlog2n satisfies φ(n) as n.

    Second, we have by standard calculations that

    m=n1φ2(m)n1x2log4xdx=O(n1log4(n))=O(nφ2(n)),

    which shows that Eq (2.5) is verified.

    Next, we have by Eq (1.1) and φ(n)=nlog2n that

    n=1P(|X1|>φ(n))=n=1P(|X1|>nlog2n)=n=1(nlog2nqx2dx+nlog2npx2dx)=n=1p+qnlog2n=n=11nlog2n<

    and then Eq (2.6) is verified.

    Finally, we also obtain by Eq (1.1) and φ(j)=jlog2j that

    1dnnj=1c1jE~Xj=1dnnj=1(djP(Xj<φ(j))+c1jEXjI(|Xj|<φ(j))+djP(Xj>φ(j)))=pqlogβnnj=1logβ2jj+pqlogβnnj=1logβ1jj=:J1+J2.

    By similar argument as in the proof of H0 in [24], we can obtain J10. By similar argument as in the proof of Eq (3.5) in [24], we can prove J2pqβ. Then we obtain by Eq (2.7) that

    1logβnnj=1logβ2jjXja.s.pqβ.

    To sum up, Theorem 1.2 is a special case of Theorem 2.2 and then Theorem 2.2 extends Theorem 1.2.

    Next, we present a new theorem of p-mean convergence for NSD random variables under some appropriate conditions, which was not considered in [24,25,26].

    Theorem 2.3. Let {Xn,n1} be a sequence of NSD random variables satisfying

    limxsupj1xαP(|Xj|>x)<,α(1,2). (2.8)

    Let {dn,n1} be a sequence of positive constants satisfying dn, and {cn,n1} be a sequence of positive constants such that cj1 and

    nj=1cαj=o(dαn). (2.9)

    Then for p(1,α),

    1dnmax1kn|kj=1c1j(XjE^Xnj)|Lp0, (2.10)

    where ^Xnj=dncjI(Xj<dncj)+XjI(|Xj|dncj)+dncjI(Xj>dncj), 1jn.

    Proof of Theorem 2.1. We first observe that for every ε>0,

    P(1Dnmax1kn|kj=1c1j(XjEXnj)|>2ε)P(max1kn|kj=1c1j(XjXnj)|>Dnε)+P(max1kn|kj=1c1j(XnjEXnj)|>Dnε)=:H1+H2.

    To prove Eq (2.3), we need only to show that Hi0 as n, i=1,2. For H1, we have by the definition of Xnj, Cn=o(Dn), Eqs (2.1) and (2.2) that

    H1P(nj=1(XjXnj))nj=1P(Xj>Dncj)=nj=11Dncj+cj=1Dn+1nj=1c1j=CnDn+10.

    For fixed n1, Xnj is the nondecreasing function of Xj. Hence, it follows by Lemma 2.1 that {Xnj,1jn} is a sequence of NSD random variables. Hence we have by Markov's inequality and Lemma 2.3 with 1<p2,

    H2CDpnE(max1kn|kj=1c1j(XnjEXnj)|)pCDpnnj=1cpjE|Xnj|p=CDpnnj=1cpjE|Xj|pI(XjDncj)+Cnj=1P(Xj>Dncj)=CDpnnj=1cpj(Dncj)p0P(|Xj|pI(XjDncj)t)dt+Cnj=11Dncj+cj=CDpnnj=1cpj(Dncj)p0P(|Xj|pt)dt+CCnDn+1=CDpnnj=1cpj(Dncj)p01t1/p+cjdt+CCnDn+1(by(2.1))CDpnnj=1cpj(Dncj)p01t1/pdt+CCnDn+1=CCnDn+CCnDn+10.

    The proof is completed.

    Proof of Theorem 2.2. Obviously, to prove Eq (2.7), we need only to show

    1dnnj=1c1j(Xj~Xj)0a.s. (3.1)

    and

    1dnnj=1c1j(~XjE~Xj)0a.s.. (3.2)

    By Eq (2.6), dn and the Borel-Cantelli lemma, we obtain

    1dnnj=1c1j|Xj|I(|Xj|>φ(j))0a.s..

    Noting that

    |Xj+φ(j)|I(Xj<φ(j))+|Xjφ(j)|I(Xj>φ(j))|Xj|I(|Xj|>φ(j)).

    Then

    |1dnnj=1c1j(Xj~Xj)|=|1dnnj=1c1jXjI(|Xj|>φ(j))+(Xj+φ(j))I(Xj<φ(j))+(Xjφ(j))I(Xj>φ(j))|2dnnj=1c1j|Xj|I(|Xj|>φ(j))0a.s.,

    which yields Eq (3.1).

    It follows by the definition of ~Xj that

    j=11φ2(j)E(~XjE~Xj)2Cj=11φ2(j)EX2jI(|Xj|φ(j))+Cj=1P(|Xj|>φ(j))=:I1+I2.

    We obtain directly by Eq (2.6) that I2<. Let F(x) be the distribution of X1, then

    I1=Cj=11φ2(j)EX21I(|X1|φ(j))=Cj=11φ2(j)x2I(|X1|φ(j))dF(x)
    =Cx2j:φ(j)|x|1φ2(j)dF(x). (3.3)

    Define N(|x|)={j:φ(j)<|x|} and j=inf{j:φ(j)|x|}. Hence we can obtain N(|x|)j1 and

    j:φ(j)|x|1φ2(j)j=j1φ2(j)Cjφ2(j)(by Eq (2.5))Cjx2
    CN(|x|)+1x2. (3.4)

    It follows by Eqs (2.6), (3.3) and (3.4) that

    I1C(N(|x|)+1)dF(x)=CEN(|X1|)+C=CE[j=1I(|X1|>φ(j))]+C=Cj=1P(|X1|>φ(j))+C<.

    Now we obtain by I1< and I2< that

    j=11φ2(j)E(~XjE~Xj)2<. (3.5)

    Consequently, by Lemma 2.4 and Eq (3.5), we get

    j=11φ(j)(~XjE~Xj)convergesa.s.,

    which implies Eq (3.2) by Kronecker's lemma, together with the condition dn.

    The proof is completed.

    Proof of Theorem 2.3. Noting that

    E{1dnmax1kn|kj=1c1j(XjE^Xnj)|}p1dpnE{max1kn|kj=1c1j(^XnjE^Xnj)|}p+1dpnE{max1kn|kj=1c1j(Xj^Xnj)|}p1dpn{E(max1kn|kj=1c1j(^XnjE^Xnj)|)2}p/2+1dpnE{max1kn|kj=1c1j(Xj^Xnj)|}p=:J1+J2.

    To prove Eq (2.10), it is sufficient to prove J10 and J20. By Lemma 2.1 and the fact that ^Xnj is the nondecreasing function of Xj, {^Xnj,1jn} is also a sequence of NSD random variables.

    We have by Lemma 2.2 that

    J2/p1=1d2nE{max1kn|kj=1c1j(^XnjE^Xnj)|}2Cd2nnj=1c2jE(^XnjE^Xnj)2Cd2nnj=1c2jEX2jI(|Xj|dncj)+Cnj=1P(|Xj|>dncj)=:J3+J4.

    By dn, Eqs (2.8) and (2.9), we have

    J4C1dαnnj=1cαj0asn. (3.6)

    Now we will show J30. Observing

    J3=Cd2nnj=1c2j(dncj)20P(X2jI(|Xj|dncj)t)dtCd2nnj=1c2j(dncj)20P(X2jt)dt.

    Let t=u2, then

    J3Cd2nnj=1c2jdncj0uP(|Xj|u)du.

    From Eq (2.8), we know that, there exists M>0 and N0N such that

    P(|Xj|u)Muαforu>N0. (3.7)

    Since dn and cj1, while n is sufficiently large, we can obtain dncj>N0. Hence

    J3Cd2nnj=1c2jN00uP(|Xj|u)du+CMd2nnj=1c2jdncjN0u1αdu=:J3+J3

    By \alpha < 2 , c_j\geq1 and Eq (2.9), we have

    \begin{eqnarray*} J_3'&\leq&\frac{C}{d_n^2}\sum\limits_{j = 1}^nc_j^{-2}\int_0^{N_0}u{\mathrm{d}}u\;\leq\;\frac{C}{d_n^2}\sum\limits_{j = 1}^nc_j^{-2}\\ &\leq&\frac{C}{d_n^{2-\alpha}}\frac{1}{d_n^{\alpha}}\sum\limits_{j = 1}^nc_j^{-\alpha}\rightarrow0\qquad\mbox{as}\quad n\rightarrow \infty \end{eqnarray*}

    and

    \begin{eqnarray*} J_3''&\leq&\frac{C}{d_n^2}\sum\limits_{j = 1}^nc_j^{-2}\bigl[(d_nc_j)^{2-\alpha}-N_0^{2-\alpha}\bigr]\\ &\leq&\frac{C}{d_n^{\alpha}}\sum\limits_{j = 1}^nc_j^{-\alpha}\rightarrow0\qquad\mbox{as}\quad n\rightarrow \infty. \end{eqnarray*}

    Finally, we need only to show J_2\rightarrow0 as n\rightarrow \infty . Let

    Z_{nj} = X_{j}-\widehat{X_{nj}} = (X_{j}+d_nc_j)\mathbb{I}(X_j < - d_nc_j)+(X_{j}-d_nc_j)\mathbb{I}(X_j > d_nc_j).

    We first prove that

    \begin{align} \mathbb{E}Z_{nj}\rightarrow0\qquad\mbox{as}\quad n\rightarrow \infty. \end{align} (3.8)

    Observing

    \begin{eqnarray*} |\mathbb{E}Z_{nj}|&\leq&\mathbb{E}|Z_{nj}|\, \leq\, \mathbb{E}|X_{j}|\mathbb{I}(|X_{j}| > d_nc_j)\\ & = &\Biggl(\int_0^{d_nc_j}+\int_{d_nc_j}^{\infty}\Biggr)\mathbb{P}(|X_{j}|\mathbb{I}(|X_{j}| > d_nc_j)\geq t) {\mathrm{d}}t\\ & = &\int_0^{d_nc_j}\mathbb{P}(|X_{j}| > d_nc_j) {\mathrm{d}}t+\int_{d_nc_j}^{\infty}\mathbb{P}(|X_{j}|\geq t) {\mathrm{d}}t\\ & = &d_nc_j\mathbb{P}(|X_{j}| > d_nc_j)+\int_{d_nc_j}^{\infty}\mathbb{P}(|X_{j}|\geq t) {\mathrm{d}}t\\ & = \;:&J_5+J_6. \end{eqnarray*}

    By Eq (3.7) and \alpha > 1 , we have

    J_5\leq \frac{M}{(d_nc_j)^{\alpha-1}}\rightarrow0\qquad\mbox{as}\quad n\rightarrow \infty

    and

    J_6\leq M\int_{d_nc_j}^{\infty}t^{-\alpha} {\mathrm{d}}t\leq\frac{CM}{(d_nc_j)^{\alpha-1}}\rightarrow0\qquad\mbox{as}\quad n\rightarrow \infty,

    which yields Eq (3.8). Therefore, we obtain by Lemma 2.3 that

    \begin{eqnarray*} J_2&\leq&\frac{1}{d_n^p}\mathbb{E}\Biggl\{\max\limits_{1\leq k\leq n}\Biggl|\sum\limits_{j = 1}^kc_j^{-1}\bigl(Z_{nj}-\mathbb{E}Z_{nj}\bigr)\Biggr|\Biggr\}^p\\ &\leq&\frac{C}{d_n^p}\sum\limits_{j = 1}^nc_j^{-p}\mathbb{E}|Z_{nj}|^p\\ &\leq&\frac{C}{d_n^p}\sum\limits_{j = 1}^nc_j^{-p}\mathbb{E}|X_{j}|^p\mathbb{I}(|X_{j}| > d_nc_j).\quad\quad(\mbox{by}\;\mbox{the}\, \mbox{definition}\, \mbox{of}\, Z_{nj}) \end{eqnarray*}

    By similar arguments as in the proof of Eq (3.8), we can obtain

    \mathbb{E}|X_{j}|^p\mathbb{I}(|X_{j}| > d_nc_j) = (d_nc_j)^p\mathbb{P}(|X_{j}| > d_nc_j)+\int_{(d_nc_j)^p}^{\infty}\mathbb{P}(|X_{j}|^p\geq t) {\mathrm{d}}t.

    Then

    \begin{eqnarray*} J_2&\leq&C\sum\limits_{j = 1}^n\mathbb{P}(|X_{j}| > d_nc_j)+\frac{C}{d_n^p}\sum\limits_{j = 1}^nc_j^{-p}\int_{(d_nc_j)^p}^{\infty}\mathbb{P}(|X_{j}|^p\geq t) {\mathrm{d}}t\\ & = \;:&J_2'+J_2''. \end{eqnarray*}

    By similar arguments as the proof of J_4\rightarrow0 , we obtain J_2'\rightarrow0 . We also have by Eq (3.7), p < \alpha and Eq (2.9) that

    \begin{eqnarray*} J_2''&\leq&\frac{C}{d_n^p}\sum\limits_{j = 1}^nc_j^{-p}\int_{(d_nc_j)^p}^{\infty}t^{-\alpha/p} {\mathrm{d}}t\\ &\leq&\frac{C}{d_n^{\alpha}}\sum\limits_{j = 1}^nc_j^{-\alpha}\rightarrow0\qquad\mbox{as}\quad n\rightarrow \infty. \end{eqnarray*}

    The proof is completed.

    In this work the author investigated the limit theorems for negatively superadditive-dependent random variables, and obtained some new results on the law of large numbers and mean convergence under some appropriate conditions. As a future work, we propose to consider some other strong convergence for sequence of negatively superadditive-dependent random variables.

    The author declares he has not used Artificial Intelligence (AI) tools in the creation of this article.

    This work is supported by the Social Sciences Planning Project of Anhui Province (AHSKY2018D98).

    The author declares that he has no conflict of interest.



    [1] GFN, Global Footprint Network, 2022. Available from: https://www.footprintnetwork.org/our-work/ecological-footprint/.
    [2] T. Li, X. Li, G. Liao, Business cycles and energy intensity. Evidence from emerging economies, Borsa Istanbul Rev., 22 (2022), 560–570. https://doi.org/10.1016/j.bir.2021.07.005 doi: 10.1016/j.bir.2021.07.005
    [3] H. C. Dai, H. B. Zhang, W. T. Wang, The impacts of U.S. withdrawal from the Paris agreement on the carbon emission space and mitigation cost of China, EU, and Japan under the constraints of the global carbon emission space, Adv. Climate Change Res., 8 (2017), 226–234. https://doi.org/10.1016/j.accre.2017.09.003 doi: 10.1016/j.accre.2017.09.003
    [4] J. Rogelj, M. D. Elzen, N. Hhne, T. Fransen, H. Fekete, H. Winkler, et al., Paris agreement climate proposals need a boost to keep warming well below 2 ℃, Nature, 534 (2016), 631–639. https://doi.org/10.1038/nature18307 doi: 10.1038/nature18307
    [5] M. N. Utomo, S. Rahayu, K. Kaujan, S. A. Irwandi, Environmental performance, environmental disclosure, and firm value: empirical study of non-financial companies at Indonesia Stock Exchange, Green Finance, 2 (2020), 100–113. https://doi.org/10.3934/GF.2020006 doi: 10.3934/GF.2020006
    [6] Z. Li, F. Zou, B. Mo, Does mandatory CSR disclosure affect enterprise total factor productivity, Econ. Res. Ekonomska Istraživanja, 2021 (2021), 1–20. https://doi.org/10.1080/1331677X.2021.2019596 doi: 10.1080/1331677X.2021.2019596
    [7] Z. Z. Li, R. Y. M. Li, M. Y. Malik, M. Murshed, Z. Khane, M. Umar, Determinants of carbon emission in China: How good is green investment, Sustainable Prod. Consumption, 27 (2021), 392–401. https://doi.org/10.1016/j.spc.2020.11.008 doi: 10.1016/j.spc.2020.11.008
    [8] M. Umar, X. Ji, D. Kirikkaleli, M. Shahbaz, X. Zhou, Environmental cost of natural resources utilization and economic growth: Can China shift some burden through globalization for sustainable development, Sustainable Dev., 28 (2020), 1678–1688. https://doi.org/10.1002/sd.2116 doi: 10.1002/sd.2116
    [9] Z. Ahmed, M. M. Asghar, M. N. Malik, K. Nawaz, Moving towards a sustainable environment: The dynamic linkage between natural resources, human capital, urbanization, economic growth, and ecological footprint in China, Resour. Policy, 67 (2020), 101677. https://doi.org/10.1016/j.resourpol.2020.101677 doi: 10.1016/j.resourpol.2020.101677
    [10] L. Wang, Y. Wang, H. Du, J. Zuo, R. Y. M. Li, Z. Zhou, et al., A comparative life-cycle assessment of hydro-, nuclear and wind power: A China study, Appl. Energ., 249 (2019), 37–45. https://doi.org/10.1016/j.apenergy.2019.04.099 doi: 10.1016/j.apenergy.2019.04.099
    [11] B. Lin, O. E. Omoju, J. U. Okonkwo, Factors influencing renewable electricity consumption in China, Renewable Sustainable Energy Rev., 55 (2016), 687–696. https://doi.org/10.1016/j.rser.2015.11.003 doi: 10.1016/j.rser.2015.11.003
    [12] W. H. Tsai, S. Y. Jhong, Carbon emissions cost analysis with activity-based costing, Sustainability, 10 (2018), 2872. https://doi:10.3390/su10082872. doi: 10.3390/su10082872
    [13] Q. Xu, Q. Cao, L. Y. Wang, Carbon market, carbon emission reduction and enterprise value—an analysis based on the valuation model and the data of Electric Power Pilot Enterprises, Fujian Tribune, 5 (2020), 151–162.
    [14] L. Lohmann, Toward a different debate in environmental accounting: The cases of carbon and cost-benefit, Accounting, Organizations Soc., 34 (2009), 499–534. https://doi.org/10.1016/j.aos.2008.03.002 doi: 10.1016/j.aos.2008.03.002
    [15] Y. L. Lin, Conception of Carbon Accounting System, MA thesis, Jimei University, 2011.
    [16] J. Lin, B. Zhang, Research on confirmation and measurement of enterprise carbon emission cost, Contemp. Econ., 1 (2012), 43–45.
    [17] J. Ratnatunga, An inconvenient truth about accounting, J. Appl. Manage. Accounting Res., 5 (2007), 1–20.
    [18] T. O'Mahony, State of the art in carbon taxes: a review of the global conclusions, Green Finance, 2 (2020), 409–423. https://doi.org/10.3934/GF.2020022 doi: 10.3934/GF.2020022
    [19] C. Park, R. Xing, T. Hanaoka, Y. Kanamori, T. Masui, Impact of energy efficient technologies on residential CO2 emissions: a comparison of Korea and China, Energy Procedia, 111 (2017), 689–698. https://doi.org/10.1016/j.egypro.2017.03.231 doi: 10.1016/j.egypro.2017.03.231
    [20] L. Wang, X. V. Vo, M. Shahbaz, A. Ak, Globalization and carbon emissions: Is there any role of agriculture value-added, financial development, and natural resource rent in the aftermath of COP21, J. Environ. Manage., 268 (2020), 110712. https://doi.org/10.1016/j.jenvman.2020.110712 doi: 10.1016/j.jenvman.2020.110712
    [21] Z. Xu, D. Zhang, S. Forbes, Z. Li, D. Seligsohn, L. West, et al., Guidelines for safe and effective carbon capture and storage in China, Energy Procedia, 4 (2011), 5966–5973. https://doi.org/10.1016/j.egypro.2011.02.599 doi: 10.1016/j.egypro.2011.02.599
    [22] H. Khajehpour, Y. Saboohi, G. Tsatsaronis, On the fair accounting of carbon emissions in the global system using an exergy cost formation concept, J. Cleaner Prod., 280 (2021), 124438. https://doi.org/10.1016/j.jclepro.2020.124438 doi: 10.1016/j.jclepro.2020.124438
    [23] H. Şimşek, G. Öztürk, Evaluation of the relationship between environmental accounting and business performance: the case of Istanbul province, Green Finance, 3 (2021), 46–58. https://doi.org/10.3934/GF.2021004 doi: 10.3934/GF.2021004
    [24] B. L. Zhang, Y. L. Lin, L. Y. Chen, Conception of carbon accounting system based on material flow analysis, Accounting Soc. China, 2010 (2010), 66–78.
    [25] Z. J. Huang, X. Ding, H. Sun, S. Y. Liu, Y. H. Liu, Analysis of factors influencing CO2 emissions of integrated iron and steel enterprises on the basis of LCA, Acta Scientiae Circumstantiae, 30 (2010), 444–448. https://doi.org/10.13671/j.hjkxxb.2010.02.010.2 doi: 10.13671/j.hjkxxb.2010.02.010.2
    [26] D. Han, L. Wang, Research on carbon cost accounting system based on the integration of life cycle cost and operation cost, Res. Finance Accounting, 9 (2015), 30–34.
    [27] Y. L. Zhang, J. B. Zeng, X. J. Fan, W. J. Chen, Discussion on measurement and practical treatment of enterprise carbon emission and carbon sequestration accounting, Accounting Res., 5 (2017), 11–18. https://doi.org/10.3969/j.issn.1003-2886.2017.05.002 doi: 10.3969/j.issn.1003-2886.2017.05.002
    [28] Y. L. Zhang, L. Y. Gu, X. Guo, Carbon audit evaluation system and its application in the iron and steel enterprises in China, J. Cleaner Prod., 248 (2020), 119204. https://doi.org/10.1016/j.jclepro.2019.119204 doi: 10.1016/j.jclepro.2019.119204
    [29] J. Ge, Y. Zhang, S. B. Yang, Research on cost-volume-benefit analysis method of carbon management accounting based on environmental capital dependence, Environ. Sci. Manage., 43 (2018), 1–5.
    [30] Y. W. Kou, Research on enterprise strategic cost management from the perspective of low-carbon economy, J. Xi'an Univ. (Social Sciences Edition), 15 (2012), 40–42. https://doi.org/10.3969/j.issn.1008-777X.2012.04.012 doi: 10.3969/j.issn.1008-777X.2012.04.012
    [31] B. Yang, F. J. Wang, K. Huang, The model of enterprise carbon emission cost suited to low-carbon economy, J. Xi'an Jiaotong Univ. (Social Science), 31 (2011), 44–47. https://doi.org/10.3969/j.issn.1008-245X.2011.01.009 doi: 10.3969/j.issn.1008-245X.2011.01.009
    [32] H. R. Zhang, X. L. Li, Research on carbon cost management from the perspective of low-carbon economy, Friend Accounting, 25 (2012), 36–37. https://doi.org/10.3969/j.issn.1004-5937.2012.25.010 doi: 10.3969/j.issn.1004-5937.2012.25.010
    [33] L. M. Cao, H. Y. Zhang, The application of resource value flow accounting in petrochemical enterprises, Finance Accounting Monthly, 13 (2015), 22–25.
    [34] I. Orji, S. Wei, A detailed calculation model for costing of green manufacturing, Ind. Manage. Data Syst., 116 (2016), 65–86. https://doi:10.1108/IMDS-04-2015-0140 doi: 10.1108/IMDS-04-2015-0140
    [35] X. Xiao, H. X. Zeng, S. H. Li, A three-dimensional model featuring material flow, value flow and organization for environmental management accounting, Accounting Res., 1 (2017), 15–22. https://doi.org/10.3969/j.issn.1003-2886.2017.01.003 doi: 10.3969/j.issn.1003-2886.2017.01.003
    [36] Z. F. Zhou, Y. Huang, S. H. Li, Classification, calculation and control of carbon cost about process manufacturing companies, World Sci-Tech R & D, 38 (2016), 403–408.
  • Reader Comments
  • © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3754) PDF downloads(212) Cited by(9)

Figures and Tables

Figures(6)  /  Tables(1)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog