A variational representation for G-Brownian functionals
Probability
2012-12-04 v3
Abstract
The purpose of this paper is to establish a variational representation \log \E [e^{f(B)}] = \sup_h \E [f(B + \int_0^{\cdot} d<B>_s h_s) - 1/2 \int_0^1 h_s \cdot (d<B>_s h_s)] for functionals of the d-dimensional G-Brownian motion B. Here \E is a sublinear expectation called G-expectation, f is any bounded function in the domain of \E mapping C([0,1];\R^d) to \R, 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.
Cite
@article{arxiv.1204.4077,
title = {A variational representation for G-Brownian functionals},
author = {Emi Osuka},
journal= {arXiv preprint arXiv:1204.4077},
year = {2012}
}