Quasi-stationary distribution for strongly Feller Markov processes by Lyapunov functions and applications to hypoelliptic Hamiltonian systems (Q6566459)

The authors consider a hypoelliptic damped Hamiltonian system and prove existence and uniqueness of a quasi-stationary distribution in special domains in \(\mathbb R^{2d}\) that look like \(O\times \mathbb R^d\), with \(O\) being some neighbourhood of a Lyapunov function minimum. The exponential convergence of the time-dependent law of the conditioned process towards this quasi-stationary distribution is shown. The stochastic process is Markov and has the strong Feller property.