Smooth linearization of contractive random dynamical systems in continuous time

TL;DR

This paper proves that uniformly exponentially stable random dynamical systems in continuous time can be smoothly conjugated to simpler systems, enhancing understanding of their long-term behavior.

Contribution

It introduces a method to smoothly linearize uniformly exponentially stable random dynamical systems in continuous time, extending previous results to a broader class.

Findings

Existence of a $C^m$ conjugacy for stable systems

Extension of linearization results to continuous-time systems

Applicable to systems with a uniformly exponentially stable linear part

Abstract

We establish that uniformly exponentially stable random dynamical systems on the half line have equivalent dynamics through a $C^m-$ conjugacy. This result was obtained for random differential equations as well as for random dynamical systems with a uniformly exponentially stable linear part.