Strong mixing measures for $C_0$-semigroups

TL;DR

This paper develops a general method to prove that certain $C_0$-semigroups admit invariant strongly mixing measures, using the Frequent Hypercyclicity Criterion, with applications to models like birth-and-death processes and the Black-Scholes equation.

Contribution

It introduces a method linking the Frequent Hypercyclicity Criterion to the existence of invariant strongly mixing measures for $C_0$-semigroups.

Findings

Establishes that the Frequent Hypercyclicity Criterion guarantees invariant strongly mixing measures.

Provides examples including birth-and-death models and the Black-Scholes equation.

Demonstrates the broad applicability of the method to various $C_0$-semigroups.

Abstract

Our purpose is to obtain a very effective and general method to prove that certain $C_0$-semigroups admit invariant strongly mixing measures. More precisely, we show that the Frequent Hypercyclicity Criterion for $C_0$-semigroups ensures the existence of invariant mixing measures with full support. We will several examples, that range from birth-and-death models to the Black-Scholes equation, which illustrate these results.