# Approximating Lyapunov exponents and stationary measures

## TL;DR

This paper presents a new proof of a theorem on the regularity of Lyapunov exponents and proposes an algorithm to approximate these exponents and stationary measures for certain random cocycles.

## Contribution

It provides a novel proof of Le Page's theorem and introduces an algorithm for approximating Lyapunov exponents and stationary measures in Bernoulli cocycles.

## Key findings

- New proof of Holder continuity of Lyapunov exponent
- Algorithm for approximating Lyapunov exponents
- Method for estimating stationary measures

## Abstract

We give a new proof of E. Le Page's theorem on the Holder continuity of the first Lyapunov exponent in the class of irreducible Bernoulli cocycles. This suggests an algorithm to approximate the first Lyapunov exponent, as well as the stationary measure, for such random cocycles.