Geodesic
Unitary representation of walks along random vector fields and the~Kolmogorov--Fokker--Planck equation in a~Hilbert space
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 2, pp. 238-257

Voir la notice de l'article provenant de la source Math-Net.Ru

Random Hamiltonian flows in an infinite-dimensional phase space is represented by random unitary groups in a Hilbert space. For this, the phase space is equipped with a measure that is invariant under a group of symplectomorphisms. The obtained representation of random flows allows applying the Chernoff averaging technique to random processes with values in the group of nonlinear operators. The properties of random unitary groups and the limit distribution for their compositions are described.
Keywords: random operator, random Hamiltonian flow, invariant measure, A. Weil theorem, Gaussian random walk, Laplace–Volterra operator, Sobolev space
Mots-clés : Kolmogorov–Fokker–Planck equation. 
@article{TMF_2024_218_2_a2,
     author = {V. M. Busovikov and Yu. N. Orlov and V. Zh. Sakbaev},
     title = {Unitary representation of walks along random vector fields and {the~Kolmogorov--Fokker--Planck} equation in {a~Hilbert} space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {218},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2024_218_2_a2/}
}
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V. M. Busovikov; Yu. N. Orlov; V. Zh. Sakbaev. Unitary representation of walks along random vector fields and the~Kolmogorov--Fokker--Planck equation in a~Hilbert space. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 2, pp. 238-257. http://geodesic.mathdoc.fr/item/TMF_2024_218_2_a2/