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Teoriya Veroyatnostei i ee Primeneniya, 2017, Volume 62, Issue 1, Pages 16–43
DOI: https://doi.org/10.4213/tvp5094 (Mi tvp5094) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Distances between stationary distributions of diffusions and solvability of nonlinear Fokker–Planck–Kolmogorov equations

V. I. Bogachevabc, A. I. Kirillovd, S. V. Shaposhnikovabc

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b St. Tikhon's Orthodox University, Moscow
c National Research University "Higher School of Economics" (HSE), Moscow
d Russian Foundation for Basic Research, Moscow
Full-text PDF (513 kB) Citations (8)
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DOI: https://doi.org/10.4213/tvp5094
Abstract: This paper is concerned with investigation of stationary distributions of diffusion processes. We obtain estimates for the Kantorovich, Prohorov, and total variation distances between stationary distributions of diffusions with different diffusion matrices and different drift coefficients. Applications are given to nonlinear stationary Fokker–Planck–Kolmogorov equations, for which new conditions for the existence and uniqueness of probability solutions are found; moreover, these conditions are optimal in a sense.
Keywords: stationary Fokker–Planck–Kolmogorov equation, total variation distance, Kantorovich metric, Prohorov metric, nonlinear Fokker–Planck–Kolmogorov equation.
Funding agency Grant number
Russian Science Foundation 14-11-00196
This work was supported by the Russian Science Foundation at Moscow State University (grant 14-11-00196).
Received: 28.06.2016
Revised: 28.07.2016
Accepted: 10.10.2016
English version:
Theory of Probability and its Applications, 2018, Volume 62, Issue 1, Pages 12–34
DOI: https://doi.org/10.1137/S0040585X97T988460
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. I. Bogachev, A. I. Kirillov, S. V. Shaposhnikov, “Distances between stationary distributions of diffusions and solvability of nonlinear Fokker–Planck–Kolmogorov equations”, Teor. Veroyatnost. i Primenen., 62:1 (2017), 16–43; Theory Probab. Appl., 62:1 (2018), 12–34
Citation in format AMSBIB
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\pages 16--43
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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