BV estimates between the quasi-stationary measure and the invariant measure for systems with small hole and additive noise

TL;DR

This paper establishes bounds on the difference between stationary and quasistationary measures in non-uniformly expanding systems with additive noise, and uses these to estimate the Lyapunov exponent.

Contribution

It introduces BV estimates for the measures and provides precise Lyapunov exponent bounds in systems with small holes and additive noise.

Findings

BV estimates between measures are established

Precise Lyapunov exponent estimates are derived

Results apply to systems with small holes and additive noise

Abstract

In this paper we introduce a class of non uniformly expanding random dynamical system with additive noise and we prove a BV estimate between the stationary measure and the quasistationary measure of the system. Furthermore, we use these bounds to give precise estimates for the Lyapunov exponent of the system.