Rough path analysis for local time of G-Brownian motion

Abstract

ABSTRACTLet be the local time of a G-Brownian motion B on a sublinear expectation space . In this paper, we show that the local time is a rough path of roughness p quasi-surely for any 2<p<3. For every Borel function g of finite q-variation (), we establish the integral as a Lyons' rough path integral. Moreover, we apply such path integrals to extend the Itô formula for a absolutely continuous function f if the derivative is bounded and left-continuous with a bounded q-variation (.