2016/06/21 by Michel Benaı̈m, Benaim, Michel, Bertrand Cloez +3 · 1 citation
Business, Management and Accounting · Economics, Econometrics and Finance · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1606.06477
openalex publication_date 2016/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the continuity of a recent paper ([6]), dealing with finite Markov chains, this paper proposes and analyzes a recursive algorithm for the approximation of the quasi-stationary distribution of a general Markov chain living on a compact metric space killed in finite time. The idea is to run the process until extinction and then to bring it back to life at a position randomly chosen according to the (possibly weighted) empirical occupation measure of its past positions. General conditions are given ensuring the convergence of this measure to the quasi-stationary distribution of the chain. We then apply this method to the numerical approximation of the quasi-stationary distribution of a diffusion process killed on the boundary of a compact set and to the estimation of the spectral gap of irreducible Markov processes. Finally, the sharpness of the assumptions is illustrated through the study of the algorithm in a non-irreducible setting.