A Mimicking Theorem for processes driven by fractional Brownian motion

TL;DR

This paper establishes a mimicking theorem for processes driven by fractional Brownian motion, providing entropy and transport estimates, and applies these to propagation of chaos and marginal dynamics in interacting SDEs.

Contribution

It introduces a new mimicking theorem for fractional Brownian motion driven processes and applies it to derive propagation of chaos and marginal dynamics formulas.

Findings

Proves a mimicking theorem for processes with fractional Brownian motion.

Provides entropy and transport estimates for these processes.

Derives sharp propagation of chaos results and marginal dynamics formulas.

Abstract

In this paper, we prove a mimicking theorem for stochastic processes with an additive Gaussian noise along with some entropy and transport type estimates. As an application of these results, we prove sharp quantitative propagation of chaos result and derive a formula for the marginal dynamics of collections of locally interacting stochastic differential equations with additive Gaussian noise.