In this paper, we establish an averaging principle on the infinite time intervals for semilinear stochastic ordinary differential equations with Lévy noise. In particular, under suitable conditions we prove that if the coefficients are Poisson stable (including periodic, quasi-periodic, almost periodic, almost automorphic etc), then there exists a unique L2-bounded solution of the original equation, which inherits the recurrence property of the coefficients, and the recurrent solution uniformly converges to the stationary solution of the averaged equation on the whole real axis in distribution sense.
Citation: Xin Liu, Yan Wang. Averaging principle on infinite intervals for stochastic ordinary differential equations with Lévy noise[J]. AIMS Mathematics, 2021, 6(5): 5316-5350. doi: 10.3934/math.2021314
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In this paper, we establish an averaging principle on the infinite time intervals for semilinear stochastic ordinary differential equations with Lévy noise. In particular, under suitable conditions we prove that if the coefficients are Poisson stable (including periodic, quasi-periodic, almost periodic, almost automorphic etc), then there exists a unique L2-bounded solution of the original equation, which inherits the recurrence property of the coefficients, and the recurrent solution uniformly converges to the stationary solution of the averaged equation on the whole real axis in distribution sense.
Monotonicity and inequalities related to complete elliptic integrals of the second kind
by Fei Wang, Bai-Ni Guo and Feng Qi. AIMS Mathematics, 2020, 5(3): 2732–2742.
DOI: 10.3934/math.2020176
In Acknowledgments section, the Grant number of "Project for Combination of Education and Research Training at Zhejiang Institute of Mechanical and Electrical Engineering" is missing. Here we give the complete information of this fund.
The changes have no material impact on the conclusion of this article. The original manuscript will be updated [1]. We apologize for any inconvenience caused to our readers by this change.
This work was partially supported by the Foundation of the Department of Education of Zhejiang Province (Grant No. Y201635387), the National Natural Science Foundation of China (Grant No. 11171307), the Visiting Scholar Foundation of Zhejiang Higher Education (Grant No. FX2018093), and the Project for Combination of Education and Research Training at Zhejiang Institute of Mechanical and Electrical Engineering (Grant No. A027120206).
The authors thank anonymous referees for their careful corrections to, helpful suggestions to, and valuable comments on the original version of this manuscript.
The authors declare that they have no conflict of interest.
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Xin Liu, Yan Wang. Averaging principle on infinite intervals for stochastic ordinary differential equations with Lévy noise[J]. AIMS Mathematics, 2021, 6(5): 5316-5350. doi: 10.3934/math.2021314
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