Convergence rate for degenerate partial and stochastic differential equations via weak Poincaré inequalities

DOI10.1016/J.JDE.2023.03.039zbMath1526.37084arXiv2110.05536OpenAlexW3205646675MaRDI QIDQ6046123

Martin Grothaus, Alexander Bertram

Publication date: 15 May 2023

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.05536

zbMATH Keywords

convergence ratemultiplicative noisedegenerate diffusion semigroupweak hypocoercivityessential dissipativity

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ordinary differential equations and systems with randomness (34F05) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Infinite-dimensional random dynamical systems; stochastic equations (37L55) Fokker-Planck equations (35Q84)

Cites Work

• Construction, ergodicity and rate of convergence of \(N\)-particle Langevin dynamics with singular potentials
• Hypocoercivity for Kolmogorov backward evolution equations and applications
• Hypercontractivity and applications for stochastic Hamiltonian systems
• Markov processes associated with \(L^{p}\)-resolvents and applications to stochastic differential equations on Hilbert space
• Hypocoercivity for kinetic equations with linear relaxation terms
• Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems.
• Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators
• Gamma calculus beyond Villani and explicit convergence estimates for Langevin dynamics with singular potentials
• Essential m-dissipativity and hypocoercivity of Langevin dynamics with multiplicative noise
• Overdamped limit of generalized stochastic Hamiltonian systems for singular interaction potentials
• Weak Poincaré inequalities for convergence rate of degenerate diffusion processes
• The theory of generalized Dirichlet forms and its applications in analysis and stochastics
• Hilbert space hypocoercivity for the Langevin dynamics revisited
• Weak Poincaré inequalities and \(L^2\)-convergence rates of Markov semigroups

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