El-Hacène Chalabi, Salim Mesbahi

On the Existence and Stability of Solutions of Stochastic Differential Systems Driven by the G-Brownian Motion

abstract:
In this paper, we study the Carathéodory approximate solution for a class of stochastic differential systems driven by G-Brownian motion. Based on the Carathéodory approximation scheme, we prove under some suitable conditions that our system has a unique solution and show that the Carathéodory approximate solutions converge to the solution of the system. Moreover, we prove a stability theorem for our system.

Mathematics Subject Classification: 60H05, 60H10, 60H30

Key words and phrases: G-expectation, G-brownian motion, G-stochastic differential equations, Carathéodory approximation scheme