Chaotic expansion in the G-expectation space

Abstract

In this paper, we are motivated by uncertainty problems in volatility. We prove the equivalent theorem of Wiener chaos with respect to $G$-Brownian motion in the framework of a sublinear expectation space. Moreover, we establish some relationship between Hermite polynomials and $G$-stochastic multiple integrals. An equivalent of the orthogonality of Wiener chaos was found.