On stochastic stability of non-uniformly expanding interval maps

TL;DR

This paper investigates the stochastic stability of non-uniformly expanding interval maps under random perturbations, establishing conditions under which these maps maintain their expanding properties despite randomness.

Contribution

It provides new theoretical results demonstrating strong stochastic stability for a broad class of non-uniformly expanding interval maps with random perturbations.

Findings

Proves stochastic stability under general conditions.

Establishes robustness of expanding properties with randomness.

Extends previous results to more general interval maps.

Abstract

We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic stability.