Quasi-stationarity and quasi-ergodicity for discrete-time Markov chains with absorbing boundaries moving periodically

William Oçafrain (1, 2)

1 UT3 - Université Toulouse III - Paul Sabatier
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We are interested in quasi-stationarity and quasi-ergodicity when the absorbing boundary is moving. First we show that, in the moving boundary case, the quasi-stationary distribution and the quasi-limiting distribution are not well-defined when the boundary is oscillating periodically. Then we show the existence of a quasi-ergodic distribution for any discrete-time irreducible Markov chain defined on a finite space state in the fixed boundary case. Finally we use this last result to show the quasi-ergodicity in the moving boundary case.

Mots clés: periodic moving boundaries; quasi-ergodic distribution; Q-process; Quasi-stationary distribution; quasi-limiting distribution; random walk

Domaines: Probabilités [math.PR]

William Oçafrain. Quasi-stationarity and quasi-ergodicity for discrete-time Markov chains with absorbing boundaries moving periodically. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2018. ⟨hal-01566428v2⟩