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Teoriya Veroyatnostei i ee Primeneniya, 2023, Volume 68, Issue 3, Pages 420–455
DOI: https://doi.org/10.4213/tvp5631 (Mi tvp5631) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Kolmogorov problems on equations for stationary and transition probabilities of diffusion processes

V. I. Bogachevab, M. Röcknerc, S. V. Shaposhnikovab

a Lomonosov Moscow State University
b HSE University, Moscow
c Bielefeld University
Full-text PDF (715 kB) Citations (5)
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DOI: https://doi.org/10.4213/tvp5631
Abstract: The paper gives a survey of several directions of research connected with the works of A. N. Kolmogorov on parabolic and elliptic Fokker–Planck–Kolmogorov equations for transition and stationary probabilities of diffusion processes. We present the fundamental results on existence of solutions, their uniqueness, and the properties of solution densities. Open questions in this area are mentioned.
Keywords: Fokker–Planck–Kolmogorov equation, transition probability, invariant measure, Cauchy problem.
Funding agency Grant number
Russian Science Foundation 22-11-00015
Contest «Young Russian Mathematics»
Received: 28.01.2023
English version:
Theory of Probability and its Applications, 2023, Volume 68, Issue 3, Pages 342–369
DOI: https://doi.org/10.1137/S0040585X97T991507
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. I. Bogachev, M. Röckner, S. V. Shaposhnikov, “Kolmogorov problems on equations for stationary and transition probabilities of diffusion processes”, Teor. Veroyatnost. i Primenen., 68:3 (2023), 420–455; Theory Probab. Appl., 68:3 (2023), 342–369
Citation in format AMSBIB
\Bibitem{BogRocSha23}
\by V.~I.~Bogachev, M.~R\"ockner, S.~V.~Shaposhnikov
\paper Kolmogorov problems on equations for stationary and transition probabilities of diffusion processes
\jour Teor. Veroyatnost. i Primenen.
\yr 2023
\vol 68
\issue 3
\pages 420--455
\mathnet{http://mi.mathnet.ru/tvp5631}
\crossref{https://doi.org/10.4213/tvp5631}
\transl
\jour Theory Probab. Appl.
\yr 2023
\vol 68
\issue 3
\pages 342--369
\crossref{https://doi.org/10.1137/S0040585X97T991507}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85179356535}
Linking options:
  • https://www.mathnet.ru/eng/tvp5631
  • https://doi.org/10.4213/tvp5631
  • https://www.mathnet.ru/eng/tvp/v68/i3/p420
    • This publication is cited in the following 5 articles:
    1. Vladimir I. Bogachev, Stanislav V. Shaposhnikov, “On reconstruction of coefficients of Fokker–Planck–Kolmogorov equations”, J. Evol. Equ., 25:1 (2025)  crossref
    2. V. I. Bogachev, S. V. Shaposhnikov, “On Reconstruction of Kolmogorov Operators with Discontinuous Coefficients”, Dokl. Math., 2024  crossref  zmath
    3. V. I. Bogachev, S. V. Shaposhnikov, “Nonlinear Fokker–Planck–Kolmogorov equations”, Russian Math. Surveys, 79:5 (2024), 751–805  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    4. V. I. Bogachev, S. V. Shaposhnikov, “On reconstruction of Kolmogorov operators with discontinuous coefficients”, Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, 516 (2024), 5  crossref
    5. V. I. Bogachev, I. I. Malofeev, S. V. Shaposhnikov, “On dependence of solutions to Fokker–Planck–Kolmogorov equations on their coefficients and initial data”, Math. Notes, 116:3 (2024), 421–431  mathnet  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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