Statistics of transitions for Markov chains with periodic forcing

TL;DR

This paper analyzes how periodic forcing affects Markov chain transition statistics, deriving explicit formulas for Floquet multipliers and applying findings to stochastic resonance phenomena.

Contribution

It provides explicit computation of Floquet multipliers for Markov chains under periodic forcing and links these to equilibrium measures, advancing understanding of stochastic resonance.

Findings

Explicit Floquet multiplier formulas derived

Connection established between multipliers and equilibrium measures

Application demonstrated in stochastic resonance context

Abstract

The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In particular the first Floquet multiplier of the associated generating function can be explicitly computed and related to the equilibrium probability measure of an associated process in higher dimension. An application to the stochastic resonance is presented.