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

Abstract

Under the framework of G-expectation and G-Brownian motion, we introduce Itô's integral for stochastic processes without assuming quasi-continuity. Then we can obtain Itô's integral on stopping time interval. This new formulation permits us to obtain Itô'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].

29 pages

References in corpus (2)

• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
• Function spaces and capacity related to a Sublinear Expectation: application to G-Brownian Motion Pathes

Cited by in corpus (3)

• Local time and Tanaka formula for G-Brownian Motion
• Self-normalized moderate deviation and laws of the iterated logarithm under G-expectation
• Backward stochastic differential equations under super linear G-expectation and associated Hamilton-Jacobi-Bellman equations