Stopping Times and Related It\^o's Calculus with G-Brownian Motion
Probability
2011-04-07 v2
Abstract
Under the framework of G-expectation and G-Brownian motion, we introduce It\^o's integral for stochastic processes without assuming quasi-continuity. Then we can obtain It\^o's integral on stopping time interval. This new formulation permits us to obtain It\^o's formula for a general C^{1,2}-function, which essentially generalizes the previous results of Peng [20, 21, 22, 23, 24] as well as those of Gao [8] and Zhang et al. [26].
Cite
@article{arxiv.0910.3871,
title = {Stopping Times and Related It\^o's Calculus with G-Brownian Motion},
author = {Xinpeng Li and Shige Peng},
journal= {arXiv preprint arXiv:0910.3871},
year = {2011}
}
Comments
29 pages