Mean exit time for the overdamped Langevin process: the case with critical points on the boundary

DOI10.1080/03605302.2021.1897841zbMath1483.31032OpenAlexW3143464287MaRDI QIDQ5012783

Boris Nectoux

Publication date: 25 November 2021

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2021.1897841

zbMATH Keywords

mean exit timeEyring-Kramers formulasoverdamped Langevin process

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Diffusion processes (60J60) Potentials and capacities on other spaces (31C15)

Related Items

The exit from a metastable state: concentration of the exit point distribution on the low energy saddle points. II, Non-reversible metastable diffusions with Gibbs invariant measure. II: Markov chain convergence, Correction

Cites Work

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• The Eyring-Kramers law for Markovian jump processes with symmetries
• Small random perturbations of finite- and infinite-dimensional dynamical systems: Unpredictability of exit times
• Metastability for a class of dynamical systems subject to small random perturbations
• Elliptic partial differential equations of second order
• Dirichlet's and Thomson's principles for non-selfadjoint elliptic operators with application to non-reversible metastable diffusion processes
• Metastability in reversible diffusion processes. I: Sharp asymptotics for capacities and exit times
• Metastability in reversible diffusion processes. II: Precise asymptotics for small eigenvalues
• Hodge decomposition. A method for solving boundary value problems
• Asymptotics of the spectra of Schrödinger operators with low temperature
• The exit from a metastable state: concentration of the exit point distribution on the low energy saddle points. I
• Asymptotic analysis of mean exit time for dynamical systems with a single well potential
• Low temperature asymptotics for quasistationary distributions in a bounded domain
• Sharp spectral asymptotics for nonreversible metastable diffusion processes
• A mathematical formalization of the parallel replica dynamics
• Metastability for parabolic equations with drift: part 1
• Kramers' law: Validity, derivations and generalisations
• Metastability for parabolic equations with drift: part II. The quasilinear case
• Tunnel effect and symmetries for Kramers–Fokker–Planck type operators
• The Eyring-Kramers law for potentials with nonquadratic saddles
• Random Perturbations of Dynamical Systems
• Perturbed Dynamical Systems with an Attracting Singularity and Weak Viscosity Limits in Hamilton-Jacobi Equations
• Exponential Leveling for Stochastically Perturbed Dynamical Systems
• Eigenvalues of the Fokker–Planck Operator and the Approach to Equilibrium for Diffusions in Potential Fields
• A Singular Perturbation Approach to Kramers’ Diffusion Problem
• The Exit Problem: A New Approach to Diffusion Across Potential Barriers
• Limiting Exit Location Distributions in the Stochastic Exit Problem
• Exponential asymptotics in the small parameter exit problem
• Spectra, exit times and long time asymptotics in the zero-white-noise limit
• On the exponential exit law in the small parameter exit problem
• Spectral Theory and its Applications
• Sharp estimate of the mean exit time of a bounded domain in the zero white noise limit
• Repartition of the Quasi-stationary Distribution and First Exit Point Density for a Double-Well Potential
• Some Problems Concerning Stability under Small Random Perturbations
• Partial differential equations and stochastic methods in molecular dynamics
• Brownian motion in a field of force and the diffusion model of chemical reactions
• Metastability