ABSTRACT
Let 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 (
.
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