A remark on quasi-ergodicity of ultracontractive Markov processes

Jinwen Chen and Siqi Jian

Statistics & Probability Letters, 2014, vol. 87, issue C, 184-190

Abstract: In this note we show that for a killed Markov process determined by a certain selfadjoint operator on a bounded domain, there are two quite different quasi-ergodic behaviors, corresponding to the Yaglom limit and a certain “fractional” Yaglom limit respectively. We also show that the high (higher than 2) order Dirichlet eigenvalues of the operator can be used to characterize the exponential convergence rate to quasi-stationarity for some marginals of the Markov process conditioned not to exit a bounded domain. These convergence rates depend on the starting points.

Keywords: Killed Markov process; Quasi-stationary distribution; Quasi-ergodicity; Dirichlet eigenvalue; Spectral gaps (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2014.01.006

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