Stochastic approximation of quasi-stationary distributions on compact spaces and applications

DOI10.1214/17-AAP1360MaRDI QIDQ1617129

Bertrand Cloez, Fabien Panloup, Michel Benaïm

Publication date: 7 November 2018

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.06477

zbMATH Keywords

reinforced random walksstochastic approximationEuler schemequasi-stationary distributionsrandom perturbations of dynamical systemsextinction rate

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Diffusion processes (60J60) Ordinary differential equations and systems with randomness (34F05) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (22)

Central Limit Theorem for stationary Fleming--Viot particle systems in finite spaces ⋮ Stochastic approximation on noncompact measure spaces and application to measure-valued Pólya processes ⋮ Monte Carlo Methods for the Neutron Transport Equation ⋮ Transcritical bifurcation for the conditional distribution of a diffusion process ⋮ Recent advances in the long-time analysis of killed degenerate processes and their particle approximation ⋮ A non‐conservative Harris ergodic theorem ⋮ General criteria for the study of quasi-stationarity ⋮ Data-driven computational methods for quasi-stationary distribution and sensitivity analysis ⋮ On the stability of positive semigroups ⋮ Stochastic generalized Kolmogorov systems with small diffusion. I: Explicit approximations for invariant probability density function ⋮ Quasi-stationary behavior for a piecewise deterministic Markov model of chemostat: the Crump-Young model ⋮ Analysis of an adaptive biasing force method based on self-interacting dynamics ⋮ Uniform convergence of penalized time-inhomogeneous Markov processes ⋮ Quasi-ergodic limits for finite absorbing Markov chains ⋮ Theoretical properties of quasi-stationary Monte Carlo methods ⋮ Regeneration-enriched Markov processes with application to Monte Carlo ⋮ Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain ⋮ An approximation scheme for quasi-stationary distributions of killed diffusions ⋮ On the Hill relation and the mean reaction time for metastable processes ⋮ On non-extinction in a Fleming-Viot-type particle model with Bessel drift ⋮ Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: Uniform estimates in a compact soft case ⋮ Approximating quasi-stationary distributions with interacting reinforced random walks

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