Rough path analysis for local time of G-Brownian motion.

Let L = { L (t , x) , t ≥ 0 , x ∈ R } be the local time of a G-Brownian motion B on a sublinear expectation space (Ω , H , E ˆ). 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 ∫ R g (x) L (t , d x) 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 f ′ is bounded and left-continuous with a bounded q-variation ( 2 ≤ q < 3). [ABSTRACT FROM AUTHOR]