Neutral stochastic partial functional integro-differential equations driven by G-Brownian motion

Abstract

In this article, we define the Hilbert-valued stochastic calculus with respect to G-Brownian motion in G-framework. On that basis, we prove the existence and uniqueness of mild solution for a class of neutral stochastic partial functional integro-differential equations driven by G-Brownian motion with non-Lipschitz coefficients. Our results are established by means of the Picard approximation. Moreover, we establish the stability of mild solution. An example is given to illustrate the theory.

Keywords

• neutral equation
• g-brownian motion
• mild solution
• stability