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Quasi-stationary distribution for strongly Feller Markov processes by Lyapunov functions and applications to hypoelliptic Hamiltonian systems

Abstract : In this paper, we establish a general result for the existence and the uniqueness of the quasi-stationary distribution of a strongly Feller Markov process killed when it exits a domain D, under some Lyapunov function condition. Our result covers the case of hypoelliptic damped Hamiltonian systems. Our method is based on the characterization of the essential spectral radius by means of Lyapunov functions and measures of non-compactness.
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https://hal.archives-ouvertes.fr/hal-03068461
Contributor : Boris Nectoux <>
Submitted on : Tuesday, December 15, 2020 - 4:23:53 PM
Last modification on : Thursday, February 25, 2021 - 10:32:02 AM

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  • HAL Id : hal-03068461, version 1

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Arnaud Guillin ♦, Boris Nectoux ♦, Liming Wu. Quasi-stationary distribution for strongly Feller Markov processes by Lyapunov functions and applications to hypoelliptic Hamiltonian systems. 2020. ⟨hal-03068461⟩

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