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A Probabilistic Characterization of g-Harmonic 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:
Citation: Liang Cai, Huan-Huan Zhang, Li-Yun Pan. A Probabilistic Characterization of g-Harmonic Functions. AIMS Mathematics, 2017, 2(1): 70-80. doi: 10.3934/Math.2017.1.70
- 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), 47-80.
- 2. Z. Chen and S. Peng, Continuous properties of g-martingales. Chin. Ann. of Math, 22 (2001), 115-128.
- 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), 1-67.
- 4. L. Jiang, Convexity, translation invariance and subadditivity for g-expectations and related risk measures. The Annals of Applied Probability, 18 (2008), 245-258.
- 5. O. D. Kellogg, Converses of Gauss’ theorem on the arithmetic mean. Tran. Amer. Math. Soc., 36(1934), 227-242.
- 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), 221-232.
- 8. S. Peng, A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation. Stochastics and Stochastic Reports, 38 (1992), 119-134.
- 9. S. Peng, BSDE and related g-expectation. Pitman Research Notes in Mathematics Series, 364, Backward Stochastic Di erential Equation, Ed. by N. El Karoui and L.Mazliak (1997), 141-159.
- 10. S. Peng, Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer’s type. Prob. Theory Rel. Fields, 113 (1999), 473-499.
- 11. S. Peng, Nonlinear expectations, nonlinear evaluations and risk measures. Stochastic Methods in Finance. Lecture Notes in Mathematics Series. 1856 (2004), 165-253.
- 12. W. Wang, Maximal inequalities for g-martingales. Statist. Probab. Lett., 79 (2009), 1169-1174.
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