Multi-Dimensional G-Brownian Motion and Related Stochastic Calculus under G-Expectation
Probability
2007-05-23 v2
Abstract
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 equation under our G-expectation.
Cite
@article{arxiv.math/0601699,
title = {Multi-Dimensional G-Brownian Motion and Related Stochastic Calculus under G-Expectation},
author = {Shige Peng},
journal= {arXiv preprint arXiv:math/0601699},
year = {2007}
}
Comments
27 pages