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TMF, 2016, Volume 189, Number 3, Pages 453–463 (Mi tmf8885)  

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

A. I. Noarov

Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

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

DOI: https://doi.org/10.4213/tmf8885

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English version:
Theoretical and Mathematical Physics, 2016, 189:3, 1796–1805

Bibliographic databases:

Received: 04.03.2015
Revised: 01.02.2016

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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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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