Rough path analysis for local time of G-Brownian motion

摘要

Let L = {L(t, x), t >= 0, x is an element of R} be the local time of a G-Brownian motion B on a sublinear expectation space (Omega, H, (E) over cap). In this paper, we show that the local time L is a rough path of roughness p quasi-surely for any 2 < p < 3. For every Borel function g of finite q-variation (2 <= q < 3), we establish the integral integral(R) g(x)L(t, dx) as a Lyons' rough path integral. Moreover, we apply such path integrals to extend the Ito formula for a absolutely continuous function f if the derivative f' is bounded and left-continuous with a bounded q-variation (2 <= q < 3).