Conditional G-expectation in $\mathbb{L}^{p}$ and related It\^o's calculus

Abstract

In this paper, we define a dynamically consistent conditional G-expectation in space $\mathbb{L}^{p}$, and give the related stochastic calculus of It\^o's type, especially get It\^o's formula for a general $C^{1,2}$-function.