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Mat. Zametki, 2014, Volume 96, Issue 5, paper published in the English version journal (Mi mz11677)  

This article is cited in 2 scientific papers (total in 2 papers)

Papers published in the English version of the journal

The Kantorovich and variation distances between invariant measures of diffusions and nonlinear stationary Fokker–Planck–Kolmogorov equations

V. I. Bogachevab, A. I. Kirillovc, S. V. Shaposhnikovba

a Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b St.-Tikhon's University, Moscow, Russia
c Russian Foundation for Basic Research, Moscow, Russia

Abstract: We obtain upper bounds for the total variation distance and the quadratic Kantorovich distance between stationary distributions of two diffusion processes with different drifts. More generally, our estimate holds for solutions to stationary Kolmogorov equations in the class of probability measures. This estimate is applied to nonlinear stationary Fokker–Planck–Kolmogorov equations for probability measures.

Keywords: Kantorovich distance, Fokker–Planck–Kolmogorov equation, invariant measure of diffusion.


English version:
Mathematical Notes, 2014, 96:5, 855–863

Bibliographic databases:

Document Type: Article
MSC: Primary 35R60; Secondary 35B35, 35Q84
Language: English

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  • http://mi.mathnet.ru/eng/mz11677

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bogachev V.I., Roeckner M., Shaposhnikov S.V., “Distances between transition probabilities of diffusions and applications to nonlinear Fokker–Planck–Kolmogorov equations”, J. Funct. Anal., 271:5 (2016), 1262–1300  crossref  mathscinet  zmath  isi  scopus
    2. V. I. Bogachev, A. I. Kirillov, S. V. Shaposhnikov, “Rasstoyaniya mezhdu statsionarnymi raspredeleniyami diffuzii i razreshimost nelineinykh uravnenii Fokkera–Planka–Kolmogorova”, Teoriya veroyatn. i ee primen., 62:1 (2017), 16–43  mathnet  crossref  mathscinet  elib
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