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

Arnaud Guillin ♦ (1) , Liming Wu (1) , Boris Nectoux ♦ (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Mots clés: Quasi-stationary distribution; strong Feller property; Lyapunov functions; essential spectral radius; hypoelliptic diffusions

Domaines: Physique mathématique [math-ph]; Probabilités [math.PR]; Théorie spectrale [math.SP]

Arnaud Guillin ♦, Liming Wu, Boris Nectoux ♦. Quasi-stationary distribution for strongly Feller Markov processes by Lyapunov functions and applications to hypoelliptic Hamiltonian systems. 2023. ⟨hal-03068461v2⟩