This paper is concerned with numerical simulations for the G- Brownian motion （defined by S. Peng in Stochastic Analysis and Applications, 2007, 541-567）. By the definition of the G-normal distribution, we first sho...This paper is concerned with numerical simulations for the G- Brownian motion （defined by S. Peng in Stochastic Analysis and Applications, 2007, 541-567）. By the definition of the G-normal distribution, we first show that the G-Brownian motions can be simulated by solving a certain kind of Hamilton-Jacobi-Bellman （HJB） equations. Then, some finite difference methods are designed for the corresponding HJB equations. Numerical simulation results of the G-normal distribution, the G-Brownian motion, and the corresponding quadratic variation process are provided, which characterize basic properties of the G-Brownian motion. We believe that the algorithms in this work serve as a fundamental tool for future studies, e.g., for solving stochastic differential equations （SDEs）/stochastic partial differential equations （SPDEs） driven by the G-Brownian motions.展开更多
In this paper, we derive a law of large numbers under the nonlinear expectation generated by backward stochastic differential equations driven by G-Brownian motion.
基金Acknowledgements The authors would like to thank the referees for their valuable comments, which improved the paper a lot. This work was partially supported by the National Natural Science Foundations of China （Grant Nos. 11171189, 11571206）.
文摘This paper is concerned with numerical simulations for the G- Brownian motion （defined by S. Peng in Stochastic Analysis and Applications, 2007, 541-567）. By the definition of the G-normal distribution, we first show that the G-Brownian motions can be simulated by solving a certain kind of Hamilton-Jacobi-Bellman （HJB） equations. Then, some finite difference methods are designed for the corresponding HJB equations. Numerical simulation results of the G-normal distribution, the G-Brownian motion, and the corresponding quadratic variation process are provided, which characterize basic properties of the G-Brownian motion. We believe that the algorithms in this work serve as a fundamental tool for future studies, e.g., for solving stochastic differential equations （SDEs）/stochastic partial differential equations （SPDEs） driven by the G-Brownian motions.
基金Supported by the National Natural Science Foundation of China(No.11211061 and No.11231005)Natural Science Foundation of Shandong Province(No.ZR2013AQ021)
文摘In this paper, we derive a law of large numbers under the nonlinear expectation generated by backward stochastic differential equations driven by G-Brownian motion.
