The Smoluchowski-Kramers limits of stochastic differential equations with irregular coefficients

DOI10.1016/j.spa.2022.04.016zbMath1495.60054OpenAlexW4229079546WikidataQ115341103 ScholiaQ115341103MaRDI QIDQ2145771

Li Yang, Longjie Xie

Publication date: 20 June 2022

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

Full work available at URL: https://doi.org/10.1016/j.spa.2022.04.016

zbMATH Keywords

homogenizationLangevin equationSmoluchowski-Kramers approximationZvonkin's transformationnoise-induced drift

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60) (L^p)-limit theorems (60F25)

Related Items (2)

Stochastic wave equation with Hölder noise coefficient: well-posedness and small mass limit ⋮ Rate of convergence in the Smoluchowski-Kramers approximation for mean-field stochastic differential equations

Cites Work

• Unnamed Item
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• The small-mass limit for Langevin dynamics with unbounded coefficients and positive friction
• Smoluchowski-Kramers approximation and large deviations for infinite-dimensional nongradient systems with applications to the exit problem
• Stochastic homeomorphism flows of SDEs with singular drifts and Sobolev diffusion coefficients
• Some remarks on the Smoluchowski-Kramers approximation
• On polynomial mixing bounds for stochastic differential equations
• On Poisson equation and diffusion approximation. II.
• Homogenization of dissipative, noisy, Hamiltonian dynamics
• Small mass asymptotic for the motion with vanishing friction
• On the Poisson equation and diffusion approximation. I
• Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems.
• Well-posedness and long time behavior of singular Langevin stochastic differential equations
• The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction
• Diffusion approximation for fully coupled stochastic differential equations
• Homogenization of nonlocal partial differential equations related to stochastic differential equations with Lévy noise
• \(L^q(L^p)\)-theory of stochastic differential equations
• Homogenization for generalized Langevin equations with applications to anomalous diffusion
• Hypoelliptic multiscale Langevin diffusions: large deviations, invariant measures and small mass asymptotics
• On the Smoluchowski-Kramers approximation for a system with an infinite number of degrees of freedom
• Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise.
• ON THE AVERAGING PRINCIPLE FOR SYSTEMS OF STOCHASTIC DIFFERENTIAL EQUATIONS
• A Homogenization Theorem for Langevin Systems with an Application to Hamiltonian Dynamics
• Ergodicity and Lyapunov Functions for Langevin Dynamics with Singular Potentials
• Multiscale Methods

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