Large deviations for the Langevin equation with strong damping

DOI10.1007/s10955-015-1346-2zbMath1329.82093arXiv1503.01027OpenAlexW3106080820MaRDI QIDQ904370

Sandra Cerrai, Mark I. Freidlin

Publication date: 13 January 2016

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.01027

zbMATH Keywords

large deviationsLaplace principleover damped stochastic differential equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Reaction-diffusion equations (35K57) Brownian motion (60J65) Large deviations (60F10) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) PDEs in connection with statistical mechanics (35Q82)

Related Items

Moderate deviations for the Langevin equations: Strong damping and fast Markovian switching ⋮ On the Smoluchowski-Kramers approximation for a system with infinite degrees of freedom exposed to a magnetic field ⋮ Large deviation principle for SDEs with Dini continuous drifts ⋮ On the small noise limit in the Smoluchowski-Kramers approximation of nonlinear wave equations with variable friction ⋮ Averaging on macroscopic scales with application to Smoluchowski-Kramers approximation ⋮ Central limit theorems and moderate deviations for stochastic reaction-diffusion lattice systems ⋮ A class of Langevin equations with Markov switching involving strong damping and fast switching ⋮ Well-posedness and long time behavior of singular Langevin stochastic differential equations ⋮ Moderate deviations for the Langevin equation with strong damping ⋮ Large deviation principles for Langevin equations in random environment and applications ⋮ Exponential tightness of a family of Skorohod integrals ⋮ Smoluchowski-Kramers approximation for the damped stochastic wave equation with multiplicative noise in any spatial dimension ⋮ Large Deviations for Nonlinear Ito Type Stochastic Integrodifferential Equations

Cites Work

• Unnamed Item
• Coupled reaction-diffusion equations
• Some remarks on the Smoluchowski-Kramers approximation
• Limit theorems for large deviations and reaction-diffusion equations
• A variational representation for certain functionals of Brownian motion
• Quasi-deterministic approximation, metastability and stochastic resonance
• The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction
• Smoluchowski-Kramers approximation in the case of variable friction
• Nonlinear stochastic perturbations of dynamical systems and quasi-linear parabolic PDE's with a small parameter
• Random Perturbations of Dynamical Systems
• Functional Integration and Partial Differential Equations. (AM-109)
• Large Deviation Principle for Singularly Perturbed Stochastic Damped Wave Equations
• SMOLUCHOWSKI–KRAMERS APPROXIMATION AND EXIT PROBLEMS