Quasi-stationary distribution for strongly Feller Markov processes by Lyapunov functions and applications to hypoelliptic Hamiltonian systems
Arnaud Guillin, Boris Nectoux, Liming Wu
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.
Topics & Concepts
MathematicsHypoelliptic operatorMarkov chainHamiltonian systemStationary distributionLyapunov functionHamiltonian (control theory)Markov processPure mathematicsMathematical analysisPartial differential equationMathematical optimizationNonlinear systemStatisticsLinear differential equationQuantum mechanicsPhysicsMarkov Chains and Monte Carlo MethodsStochastic processes and statistical mechanicsMathematical Dynamics and Fractals