RESEARCH ARTICLE

Numerical simulations for G-Brownian motion

  • Jie YANG ,
  • Weidong ZHAO
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  • School of Mathematics & Finance Institute, Shandong University, Jinan 250100, China

Received date: 28 Apr 2015

Accepted date: 19 Oct 2015

Published date: 18 Oct 2016

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

This paper is concerned with numerical simulations for the GBrownian 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.

Cite this article

Jie YANG , Weidong ZHAO . Numerical simulations for G-Brownian motion[J]. Frontiers of Mathematics in China, 2016 , 11(6) : 1625 -1643 . DOI: 10.1007/s11464-016-0504-9

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