Law Of Large Numbers For Random Dynamical Systems

TL;DR

This paper proves the existence of an exponentially attractive invariant measure and a strong law of large numbers for a class of random dynamical systems with position-dependent jumps.

Contribution

It establishes the strong law of large numbers and invariant measure existence for random dynamical systems with position-dependent jumps, advancing understanding of their long-term behavior.

Findings

Existence of an exponentially attractive invariant measure.

Proof of the strong law of large numbers.

Applicable to systems with position-dependent jumps.

Abstract

We cosider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. We proove the existence of an exponentially attractive invariant measure and the strong law of large numbers.