Renormalization Group Method for Singular Perturbed Systems Driven by Fractional Brownian Motion

Abstract

In this article, we use the renormalization group method to study the approximate solution of stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter H∈12,1. We derive a related reduced system, which we use to construct the separate scale approximation solutions. It is shown that the approximate solutions remain valid with high probability on large time scales. We also expect that our general approach can be applied to the fields of physics, finance, and engineering, etc.