Recent advances in the long-time analysis of killed degenerate processes and their particle approximation

2023/05/25 by Bertrand Cloez, Cloez, Bertrand, Lucas Journel +7
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2305.15915

openalex publication_date 2023/05/25 · openalex created_date 2023/05/27 · openalex updated_date 2026/07/28

Abstract

We review some recent results of quantitative long-time convergence for the law of a killed Markov process conditioned to survival toward a quasi-stationary distribution, and on the analogous question for the particle systems used in practice to sample these distributions. With respect to the existing literature, one of the novelties of these works is the degeneracy of the underlying process with respect to classical elliptic diffusion, namely it can be a non-elliptic hypoelliptic diffusion, a piecewise deterministic Markov process or an Euler numerical scheme.

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• Quasi-Stationary Distributions of Interacting Dynamical Systems and their approximation

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