Stopping Times and Related Itô's Calculus with G-Brownian Motion

Details Stopping Times and Related Itô's Calculus with G-Brownian Motion Stopping Times and Related Itô's Calculus with G-Brownian Motion

2009-10-20

arxiv.org/abs/0910.3871v2

Mathematics

Probability

29 pages

Scientific paper

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].

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