
AIMS Mathematics, 2017, 2(1): 7080. doi: 10.3934/Math.2017.1.70
Research article
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
A Probabilistic Characterization of gHarmonic Functions
1 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
2 Department of Basic Science, Beijing Institute of Graphic Communication, Beijing 102600, China
3 Beijing Institute of Education, Beijing 100120, China
Received: , Accepted: , Published:
References
1. G. Barles and E. Lesigne, SDE, BSDE and PDE. Pitman Research Notes in Mathematics Series, 364, Backward Stochastic Differential Equation, Ed. by N. El Karoui and L.Mazliak (1997), 4780.
2. Z. Chen and S. Peng, Continuous properties of gmartingales. Chin. Ann. of Math, 22 (2001), 115128.
3. M. G. Crandall, H. Ishii and P. L. Lions, User's guide to viscosity solutions of second order Partial differential equations. Bull. Amer. Math. Soc., 27 (1992), 167.
4. L. Jiang, Convexity, translation invariance and subadditivity for gexpectations and related risk measures. The Annals of Applied Probability, 18 (2008), 245258.
5. O. D. Kellogg, Converses of Gauss' theorem on the arithmetic mean. Tran. Amer. Math. Soc., 36(1934), 227242.
6. B. Øksendal, Stochastic differential Equations, Sixth Edition, Springer, Berlin, 2003.
7. B. Øksendal and D. W. Stroock, A characterization of harmonic measure and markov processs whose hitting distritributions are preserved by rotations, translations and dilatations. Ann. Inst. Fourier. 32 (1982), 221232.
8. S. Peng, A generalized dynamic programming principle and HamiltonJacobiBellman equation. Stochastics and Stochastic Reports, 38 (1992), 119134.
9. S. Peng, BSDE and related gexpectation. Pitman Research Notes in Mathematics Series, 364, Backward Stochastic Di erential Equation, Ed. by N. El Karoui and L.Mazliak (1997), 141159.
10. S. Peng, Monotonic limit theorem of BSDE and nonlinear decomposition theorem of DoobMeyer's type. Prob. Theory Rel. Fields, 113 (1999), 473499.
11. S. Peng, Nonlinear expectations, nonlinear evaluations and risk measures. Stochastic Methods in Finance. Lecture Notes in Mathematics Series. 1856 (2004), 165253.
12. W. Wang, Maximal inequalities for gmartingales. Statist. Probab. Lett., 79 (2009), 11691174.
Copyright Info: © 2017, Liang Cai, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)