Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

The Poisson Equation and Estimates for Distances Between Stationary Distributions of Diffusions

The Poisson Equation and Estimates for Distances Between Stationary Distributions of Diffusions We estimate distances between stationary solutions to Fokker–Planck–Kolmogorov equations with different diffusion and drift coefficients. To this end we study the Poisson equation on the whole space. We have obtained sufficient conditions for stationary solutions to satisfy the Poincaré and logarithmic Sobolev inequalities. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Sciences Springer Journals

The Poisson Equation and Estimates for Distances Between Stationary Distributions of Diffusions

Download PDF
29 pages

Loading next page...
 
/lp/springer_journal/the-poisson-equation-and-estimates-for-distances-between-stationary-6kkzCH0kh1
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1072-3374
eISSN
1573-8795
DOI
10.1007/s10958-018-3872-3
Publisher site
See Article on Publisher Site

Abstract

We estimate distances between stationary solutions to Fokker–Planck–Kolmogorov equations with different diffusion and drift coefficients. To this end we study the Poisson equation on the whole space. We have obtained sufficient conditions for stationary solutions to satisfy the Poincaré and logarithmic Sobolev inequalities.

Journal

Journal of Mathematical Sciences – Springer Journals

Published: Jun 2, 2018

References

  • The Kantorovich and variation distances between invariant measures of diffusions and nonlinear stationary Fokker-Planck-Kolmogorov equations
    Bogachev, VI; Kirillov, AI; Shaposhnikov, SV
  • A simple proof of the Poincaré inequality for a large class of probability measures
    Bakry, D; Barthe, F; Cattiaux, P; Guillin, A
  • Hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic Ising models
    Deuschel, J-D; Stroock, DW
  • Poincaré–Chernoff type inequalities for reversible probability measures of diffusion processes
    LIn, TF; Huang, MJ
  • Dimension dependent hypercontractivity for Gaussian kernels
    Bakry, D; Bolley, F; Gentil, I
  • Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré
    Bakry, D; Cattiaux, P; Guillin, A
  • Phi-entropy inequalities for diffusion semigroups
    Bolley, F; Gentil, I
  • Poincaré inequality and the L p convergence of semi-groups
    Cattiaux, P; Guillin, A; Roberto, C
  • Lyapunov conditions for super Poincaré inequalities
    Cattiaux, P; Guillin, A; Wang, F-Y; Wu, L
  • On an integral criterion for hypercontractivity of diffusion semigroups and extremal functions
    Ledoux, M
  • Convex Sobolev inequalities derived from entropy dissipation
    Matthes, D; Jüngel, A; Toscani, G
  • Harnack and functional inequalities for generalized Mehler semigroups
    Röckner, M; Wang, F-Y
  • Analysis and Geometry on Groups
    Varopoulos, NT; Saloff-Coste, L; Coulhon, T
  • Functional Inequalities, Markov Semigroups and Spectral Theory
    Wang, F-Y
  • Entropy-cost inequalities for diffusion semigroups with curvature unbounded below
    Wang, F-Y
  • From super Poincaré to weighted log-Sobolev and entropy-cost inequalities
    Wang, F-Y
  • On the Poisson equation and diffusion approximation. I
    Pardoux, E; Veretennikov, AY
  • Distances between transition probabilities of diffusions and applications to nonlinear Fokker–Planck–Kolmogorov equations
    Bogachev, VI; Röckner, M; Shaposhnikov, SV
  • Stability of densities for perturbed diffusions and Markov chains
    Konakov, V; Kozhina, A; Menozzi, S
  • Elliptic and parabolic equations for measures
    Bogachev, VI; Krylov, NV; Röckner, M
  • The Monge–Kantorovich problem: achievements, connections, and perspectives
    Bogachev, VI; Kolesnikov, AV
  • Measure Theory. Vol. 1 and 2
    Bogachev, VI
  • Isoperimetric and analytic inequalities for log-concave probability measures
    Bobkov, SG
  • Global Lipschitz regularizing effects for linear and nonlinear parabolic equations
    Porretta, A; Priola, E
  • Global properties of invariant measures
    Metafune, G; Pallara, D; Rhandi, A
  • General logarithmic Sobolev inequalities and Orlicz imbeddings
    Adams, RA
  • Measure Theory and Fine Properties of Functions
    Evans, CL; Gariepy, RF