Non-stationary version of Ergodic Theorem for random dynamical systems

TL;DR

This paper extends the classical Ergodic Theorem to non-stationary random dynamical systems, providing a theoretical foundation for analyzing systems where statistical properties change over time.

Contribution

It introduces a non-stationary version of the pointwise Ergodic Theorem and demonstrates its applicability to non-stationary iterated function systems and matrix products.

Findings

Established a non-stationary Ergodic Theorem for random dynamical systems

Applied the theorem to non-stationary iterated function systems

Applied the theorem to non-stationary random matrix products

Abstract

We prove a version of pointwise Ergodic Theorem for non-stationary random dynamical systems. Also, we discuss two specific examples where the result is applicable: non-stationary iterated function systems and non-stationary random matrix products.