A Trajectorial Approach to the Gradient Flow Properties of Langevin--Smoluchowski Diffusions

DOI10.1137/S0040585X97T990678zbMath1480.60237arXiv2008.09220OpenAlexW3080717435MaRDI QIDQ5034425

Ioannis Karatzas, Bertram Tschiderer, Walter Schachermayer

Publication date: 25 February 2022

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.09220

zbMATH Keywords

relative entropygradient flowFisher informationfunctional inequalitiesdiffusion processestime reversalWasserstein distanceoptimal transport

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Diffusion processes (60J60)

Related Items (2)

Trajectorial dissipation of \({\Phi}\)-entropies for interacting particle systems ⋮ A trajectorial approach to relative entropy dissipation of McKean-Vlasov diffusions: gradient flows and HWBI inequalities

Cites Work

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• A trajectorial interpretation of the dissipations of entropy and Fisher information for stochastic differential equations
• A gradient flow approach to large deviations for diffusion processes
• A trajectorial interpretation of Doob's martingale inequalities
• Entropy production by block variable summation and central limit theorems
• Stochastic methods. A handbook for the natural and social sciences
• Time reversal of diffusions
• Stochastic control and nonequilibrium thermodynamical systems
• Some applications of mass transport to Gaussian-type inequalities
• A convexity principle for interacting gases
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• The Fokker-Planck equation. Methods of solutions and applications.
• Dynamical aspects of the generalized Schrödinger problem via Otto calculus -- a heuristic point of view
• Trajectorial dissipation and gradient flow for the relative entropy in Markov chains
• An entropic interpolation proof of the HWI inequality
• Pathwise versions of the Burkholder-Davis-Gundy inequality
• The numéraire portfolio in semimartingale financial models
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Zur Umkehrbarkeit der statistischen Naturgesetze
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Some inequalities satisfied by the quantities of information of Fisher and Shannon
• Smooth Transition Densities for One-Dimensional Diffusions
• Variational path-integral representations for the density of a diffusion process
• Singular Perturbation Methods in Stochastic Differential Equations of Mathematical Physics
• Polar factorization and monotone rearrangement of vector‐valued functions
• Probability with Martingales
• The Variational Formulation of the Fokker--Planck Equation
• Some Properties of Path Measures
• On the convexity of the entropy along entropic interpolations
• Transport Inequalities. A Survey
• Elements of Information Theory
• Large deviations and gradient flows
• Optimal Transport

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