Geodesic
Recent advances in the long-time analysis of killed degenerate processes and their particle approximation
Bertrand Cloez1 ; Lucas Journel2 ; Pierre Monmarche3 ; Boris Nectoux4 ; Mouad Ramil5
1 MISTEA, Université Montpellier, INRAE, Institut Agro, Montpellier, France
2 LJLL, Sorbonne Université, Paris
3 LJLL and LCT, Sorbonne Université, Paris
4 LMBP, Université Clermont Auvergne
5 CERMICS, Ecole des Ponts, Marne-la-Vallée, France
ESAIM. Proceedings, Tome 75 (2023), pp. 60-85.

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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.
DOI : 10.1051/proc/202375060

Bertrand Cloez 1 ; Lucas Journel 2 ; Pierre Monmarche 3 ; Boris Nectoux 4 ; Mouad Ramil 5

1 MISTEA, Université Montpellier, INRAE, Institut Agro, Montpellier, France
2 LJLL, Sorbonne Université, Paris
3 LJLL and LCT, Sorbonne Université, Paris
4 LMBP, Université Clermont Auvergne
5 CERMICS, Ecole des Ponts, Marne-la-Vallée, France 
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     title = {Recent advances in the long-time analysis of killed degenerate processes and their particle approximation},
     journal = {ESAIM. Proceedings},
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Bertrand Cloez; Lucas Journel; Pierre Monmarche; Boris Nectoux; Mouad Ramil. Recent advances in the long-time analysis of killed degenerate processes and their particle approximation. ESAIM. Proceedings, Tome 75 (2023), pp. 60-85. doi : 10.1051/proc/202375060. http://geodesic.mathdoc.fr/articles/10.1051/proc/202375060/

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