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We are interested in quasi-stationarity and quasi-ergodicity when theabsorbing boundary is moving. First we show that, in the moving boundary case,the quasi-stationary distribution and the quasi-limiting distribution are notwell-defined when the boundary is oscillating periodically. Then we show theexistence of a quasi-ergodic distribution for any discrete-time irreducibleMarkov 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 movingboundary case.

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