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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 3, Pages 453–463
DOI: https://doi.org/10.4213/tmf8885 (Mi tmf8885) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Stationary Fokker–Planck equation on noncompact manifolds and in unbounded domains

A. I. Noarov

Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia
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DOI: https://doi.org/10.4213/tmf8885
Abstract: We investigate the Fokker–Planck equation on an infinite cylindrical surface and in an infinite strip with reflecting boundary conditions, prove the existence of a positive (not necessarily integrable) solution, and derive various conditions on the vector field $\mathbf f$ that are sufficient for the existence of a solution that is the probability density. In particular, these conditions are satisfied for some vector fields $\mathbf f$ with integral trajectories going to infinity.
Keywords: diffusion process, stationary distribution, elliptic equation for measures, averaging method.
Received: 04.03.2015
Revised: 01.02.2016
English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 3, Pages 1796–1805
DOI: https://doi.org/10.1134/S0040577916120114
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. I. Noarov, “Stationary Fokker–Planck equation on noncompact manifolds and in unbounded domains”, TMF, 189:3 (2016), 453–463; Theoret. and Math. Phys., 189:3 (2016), 1796–1805
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v189/i3/p453
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:68
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