Almost Periodic Solutions for Stochastic Differential Equations Driven By G-Brownian Motion

Abstract

In this paper, we introduce the concept of the p-mean almost periodicity for stochastic processes in non linear expectation spaces. The existence and uniqueness of square-mean almost periodic solutions to some non linear stochastic differential equations driven by G-Brownian motion are established under some assumptions for the coefficients. The asymptotic stability of the unique square-mean almost periodic solution in the square-mean sense is also discussed.

Keywords:

• G-Brownian motion
• Non linear expectation
• p-Mean almost periodicity
• Stochastic differential equation

Mathematics Subject Classification:

• 60H20
• 34C27
• 34G20