Quasi-stationary distribution for the Langevin process in cylindrical domains. I: Existence, uniqueness and long-time convergence

DOI10.1016/j.spa.2021.11.005zbMath1481.35294arXiv2101.11999OpenAlexW3212845829MaRDI QIDQ2066964

Julien Reygner, Mouad Ramil, Tony Lelièvre

Publication date: 17 January 2022

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.11999

zbMATH Keywords

compactnessspectral decompositionquasi-stationary distributionLangevin process

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) General topics in linear spectral theory for PDEs (35P05) Linear operators defined by compactness properties (47B07) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (6)

A probabilistic study of the kinetic Fokker-Planck equation in cylindrical domains ⋮ Quasi-stationary distribution for the Langevin process in cylindrical domains. II: Overdamped limit ⋮ Non-reversible metastable diffusions with Gibbs invariant measure. II: Markov chain convergence ⋮ 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 ⋮ Quasi-stationary distribution for Hamiltonian dynamics with singular potentials

Cites Work

• Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinc\-tion
• Generalisation of the Eyring-Kramers transition rate formula to irreversible diffusion processes
• Uniform conditional ergodicity and intrinsic ultracontractivity
• Quasi-stationary distributions and diffusion models in population dynamics
• On the convergence of diffusion processes conditioned to remain in a bounded region for large time to limiting positive recurrent diffusion processes
• Killed diffusions and their conditioning
• The Green function for uniformly elliptic equations
• Elliptic partial differential equations of second order
• Quasi-stationary distributions and population processes
• Sharp asymptotics of the first exit point density
• Molecular dynamics. With deterministic and stochastic numerical methods
• A mathematical formalization of the parallel replica dynamics
• Quasi-Stationary Distributions
• Tunnel effect and symmetries for Kramers–Fokker–Planck type operators
• Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries
• Criteria for Exponential Convergence to Quasi-Stationary Distributions and Applications to Multi-Dimensional Diffusions
• Ergodic Properties of Markov Processes
• The Art of Molecular Dynamics Simulation
• Partial differential equations and stochastic methods in molecular dynamics
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