PDE Seminar

Abstract

This paper is devoted to the Wong-Zakai approximations for a class of rough differential equations driven by fractional Brownian rough path ω with Hurst index H ∈(1/3, 1/2). We first construct the approximation ω_ δ of ω by probabilistic arguments, and then using the rough path theory to obtain the Wong-Zakai approximation for the solution on any finite interval. Finally, both the original system and approximated system generate a random dynamical system ϕ and ϕ^δ. As a consequence of the Wong-Zakai approximation of the solution, ϕ^δ converges to ϕ as δ → 0.