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

The Poisson Equation and Estimates for Distances Between Stationary Distributions of Diffusions DOI 10.1007/s10958-018-3872-3 Journal of Mathematical Sciences, Vol. 232, No. 3, July, 2018 THE POISSON EQUATION AND ESTIMATES FOR DISTANCES BETWEEN STATIONARY DISTRIBUTIONS OF DIFFUSIONS V. I. Bogachev Moscow State University, Moscow 119991, Russia National University Higher School of Economics 20, Myasnitskaya St., Moscow 101000, Russia St. Tikhon’s Orthodox Humanitarian University 23-5A, Novokuznetskaya St., Moscow 115184, Russia vibogach@mail.ru M. R¨ ockner Universit¨ at Bielefeld, Bielefeld 33501, Germany roeckner@math.uni-bielefeld.de S. V. Shaposhnikov Moscow State University, Moscow 119991, Russia National University Higher School of Economics 20, Myasnitskaya St., Moscow 101000, Russia St. Tikhon’s Orthodox Humanitarian University 23-5A, Novokuznetskaya St., Moscow 115184, Russia starticle@mail.ru UDC 517.95 We estimate distances between stationary solutions to Fokker–Planck–Kolmogorov equa- tions 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 so- lutions to satisfy the Poincar´e and logarithmic Sobolev inequalities. Bibliography:35 titles. Dedicated to the memory of Vasilii Vasil’evich Zhikov 1 Introduction Let us consider two Borel probability measures μ and σ on R satisfying the stationary Fokker– ∗ ∗ ∗ ∗ Planck–Kolmogorov equations L μ =0 and L σ =0, where L and L are formally adjoint μ σ μ σ 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

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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
D.O.I.
10.1007/s10958-018-3872-3
Publisher site
See Article on Publisher Site

Abstract

DOI 10.1007/s10958-018-3872-3 Journal of Mathematical Sciences, Vol. 232, No. 3, July, 2018 THE POISSON EQUATION AND ESTIMATES FOR DISTANCES BETWEEN STATIONARY DISTRIBUTIONS OF DIFFUSIONS V. I. Bogachev Moscow State University, Moscow 119991, Russia National University Higher School of Economics 20, Myasnitskaya St., Moscow 101000, Russia St. Tikhon’s Orthodox Humanitarian University 23-5A, Novokuznetskaya St., Moscow 115184, Russia vibogach@mail.ru M. R¨ ockner Universit¨ at Bielefeld, Bielefeld 33501, Germany roeckner@math.uni-bielefeld.de S. V. Shaposhnikov Moscow State University, Moscow 119991, Russia National University Higher School of Economics 20, Myasnitskaya St., Moscow 101000, Russia St. Tikhon’s Orthodox Humanitarian University 23-5A, Novokuznetskaya St., Moscow 115184, Russia starticle@mail.ru UDC 517.95 We estimate distances between stationary solutions to Fokker–Planck–Kolmogorov equa- tions 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 so- lutions to satisfy the Poincar´e and logarithmic Sobolev inequalities. Bibliography:35 titles. Dedicated to the memory of Vasilii Vasil’evich Zhikov 1 Introduction Let us consider two Borel probability measures μ and σ on R satisfying the stationary Fokker– ∗ ∗ ∗ ∗ Planck–Kolmogorov equations L μ =0 and L σ =0, where L and L are formally adjoint μ σ μ σ

Journal

Journal of Mathematical SciencesSpringer Journals

Published: Jun 2, 2018

References

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