A trajectorial interpretation of the dissipations of entropy and Fisher information for stochastic differential equations

DOI10.1214/14-AOP969zbMath1351.60070arXiv1107.3300OpenAlexW2963432572MaRDI QIDQ272943

Benjamin Jourdain, Joaquin Fontbona

Publication date: 21 April 2016

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.3300

zbMATH Keywords

stochastic differential equationslong-time behaviortime reversalcontinuous-time Markov processesbackward martingalesBakry-Emery criterionconvex Sobolev inequalitiesGirsanov theorysubmartingales

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Asymptotic behavior of solutions to PDEs (35B40) Generalizations of martingales (60G48) Applications of stochastic analysis (to PDEs, etc.) (60H30) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Martingales with continuous parameter (60G44) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (15)

A Trajectorial Approach to the Gradient Flow Properties of Langevin--Smoluchowski Diffusions ⋮ Trend to Equilibrium for Reaction-Diffusion Systems Arising from Complex Balanced Chemical Reaction Networks ⋮ A Variational Characterization of Langevin-Smoluchowski Diffusions ⋮ Mean field limit and propagation of chaos for Vlasov systems with bounded forces ⋮ Semi Log-Concave Markov Diffusions ⋮ Optimal non-reversible linear drift for the convergence to equilibrium of a diffusion ⋮ Time Reversal of diffusion processes under a finite entropy condition ⋮ Trajectorial dissipation of \({\Phi}\)-entropies for interacting particle systems ⋮ Hypocoercivity and fast reaction limit for linear reaction networks with kinetic transport ⋮ The entropy method for reaction-diffusion systems without detailed balance: first order chemical reaction networks ⋮ Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction-diffusion systems ⋮ Quantitative estimates of propagation of chaos for stochastic systems with \(W^{-1,\infty}\) kernels ⋮ Fractional-Diffusion--Advection Limit of a Kinetic Model ⋮ Time reversal of Markov processes with jumps under a finite entropy condition ⋮ A trajectorial approach to relative entropy dissipation of McKean-Vlasov diffusions: gradient flows and HWBI inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Accelerating diffusions
• Calcul stochastique et problèmes de martingales
• Time reversal of infinite-dimensional diffusions
• Time reversal of diffusions
• Dirichlet forms and analysis on Wiener space
• Minimization of the Kullback information of diffusion processes
• A pathwise approach of some classical inequalities
• Integration by parts and time reversal for diffusion processes
• Logarithmic Sobolev inequalities and stochastic Ising models
• Entropies, convexity, and functional inequalities: on \(\Phi\)-entropies and \(\Phi\)-Sobolev inequalities
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS

This page was built for publication: A trajectorial interpretation of the dissipations of entropy and Fisher information for stochastic differential equations