A variational representation for G-Brownian functionals
Abstract
The purpose of this paper is to establish a variational representation [ef(B)] = h [f(B + ∫0· d<B>s hs) - 1/2 ∫01 hs · (d<B>s hs)] for functionals of the d-dimensional G-Brownian motion B. Here is a sublinear expectation called G-expectation, f is any bounded function in the domain of mapping C([0,1];d) to , the integrals are taken with respect to the quadratic variation of B, and the supremum runs over all h's for which these integrals are well-defined. As an application, we give another proof of the results obtained by Gao-Jiang (2010), large deviations for G-Brownian motion.
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