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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
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
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
Linking options:
https://www.mathnet.ru/eng/tmf8885https://doi.org/10.4213/tmf8885 https://www.mathnet.ru/eng/tmf/v189/i3/p453
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Abstract page: | 397 | Full-text PDF : | 144 | References: | 59 | First page: | 21 |
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