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Quasi-stationary distribution for strongly Feller Markov processes by Lyapunov functions and applications to hypoelliptic Hamiltonian systems
Arnaud Guillin, Boris Nectoux, Liming Wu
Source abstract
We establish a general result on the existence and uniqueness of a quasi-stationary distribution \mu_{\mathcal{D}} of a strongly Feller Markov process (X_{t},t\ge 0) killed when it exits a domain \mathcal{D} , under some Lyapunov function condition. Our result covers the case of hypoelliptic damped Hamiltonian systems. Our method is based on a characterization of the essential spectral radius by means of Lyapunov functions and measures of noncompactness.
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