Geodesic
Stationary Fokker--Planck equation on noncompact manifolds and in unbounded domains
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 3, pp. 453-463

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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.
Mots-clés : diffusion process
Keywords: stationary distribution, elliptic equation for measures, averaging method. 
@article{TMF_2016_189_3_a10,
     author = {A. I. Noarov},
     title = {Stationary {Fokker--Planck} equation on noncompact manifolds and in unbounded domains},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {453--463},
     publisher = {mathdoc},
     volume = {189},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_189_3_a10/}
}
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A. I. Noarov. Stationary Fokker--Planck equation on noncompact manifolds and in unbounded domains. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 3, pp. 453-463. http://geodesic.mathdoc.fr/item/TMF_2016_189_3_a10/