English

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].

Keywords

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}
}

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29 pages