Stability and averaging principle for distribution dependent SDEs driven by G-Brownian motion

Abstract

This paper concerns the asymptotic behavior for distribution dependent stochastic differential equations driven by G-Brownian motion (G-SDEs). Under Lipschitz condition, we study exponentially second-moment ultimate boundedness, stability and averaging principle. Under non-Lipschitz condition, we first prove the existence and uniqueness for distribution dependent G-SDEs by adopting Carathéodory approximation approach. In particular, the fast time oscillating distribution dependent G-SDEs is treated and its solution can be approximated by the averaged distribution dependent G-SDEs under averaging condition. Additionally, two illustrative examples are provided to validate the averaged-distribution-dependent G-SDEs.