Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:118

Article

Peng, Shige

关键词: g-expectation;    G-expectation;    G-normal distribution;    BSDE;    SDE;    Nonlinear probability theory;    Nonlinear expectation;    Brownian motion;    Ito's stochastic calculus;    Ito's integral;    Ito's formula;    Gaussian process;    Quadratic variation process;    Jensen's inequality;    G-convexity;   

DOI  :  10.1016/j.spa.2007.10.015

来源: Elsevier

【 摘 要 】

We develop a notion of nonlinear expectation - G-expectation - generated by a nonlinear heat equation with infinitesimal generator G. We first study multi-dimensional G-normal distributions. With this nonlinear distribution we can introduce Our G-expectation under which the canonical process is a multi-dimensional G-Brownian motion. We then establish the related stochastic calculus, especially stochastic integrals of Ito's type with respect to Our G-Brownian motion, and derive the related Ito's formula. We have also obtained the existence and uniqueness of stochastic differential equations under Our G-expectation. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free