Multiple G-Itô integral in G-expectation space

Abstract

In 2007, Peng introduced Itô integral with respect to G-Brownian motion and the related Itô’s formula in G-expectation space. Motivated by the properties of multiple Wiener integral obtained by Itô in 1951, we introduce multiple G-Itô integral in G-expectation space, and investigate how to calculate it. Furthermore, We establish a relationship between Hermite polynomials and multiple G-Itô integrals.

Key words： Sublinear expectation; G-Brownian motion; Itô integral; Hermite polynomial

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