6533b7d0fe1ef96bd125a4a5

RESEARCH PRODUCT

Statistics of transitions for Markov chains with periodic forcing

Damien LandonSamuel Herrmann

subject

[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Markov chain mixing timeMarkov kernelMarkov chainProbability (math.PR)Markov chainlarge time asymptoticStochastic matrixcentral limit theoremMarkov process[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]symbols.namesakeMarkov renewal processModeling and SimulationFloquet multipliersStatisticsFOS: MathematicssymbolsMarkov propertyExamples of Markov chainsstochastic resonance60J27 60F05 34C25[ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]Mathematics - ProbabilityMathematics

description

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.

yearjournalcountryeditionlanguage
2013-03-26
https://hal.archives-ouvertes.fr/hal-00804847v2/document