Geodesic
Corrections to the diffusion approximation in stochastic differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 2, pp. 211-223 
S. E. Pitovranov; V. N. Chetverikov. Corrections to the diffusion approximation in stochastic differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 2, pp. 211-223. http://geodesic.mathdoc.fr/item/TMF_1978_35_2_a6/
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     title = {Corrections to the diffusion approximation in stochastic differential equations},
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     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1978_35_2_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

An investigation is made of a system of Stochastic ordinary differential equations with a coordinate- and time-dependent Gaussian random field of velocities that differs little from one which is delta-correlated with respect to the time. The resulting corrections to the Einstein–Fokker–Planck–Kolmogorov equation are found explicitly, and some consequences of these corrections are discussed.

[1] R. L. Stratonovich, Izbrannye voprosy teorii fluktuatsii v radiotekhnike, «Sov. radio», 1961 | Zbl

[2] R. L. Stratonovich, Uslovnye markovskie protsessy i ikh primenenie k teorii optimalnogo upravleniya, MGU, 1966 | MR

[3] S. M. Rytov, Vvedenie v statisticheskuyu radiofiziku, ch. 1, «Nauka», 1976 | MR

[4] V. I. Klyatskin, Statisticheskoe opisanie dinamicheskikh sistem s fluktuiruyuschimi parametrami, «Nauka», 1975

[5] K. Furutsu, J. Res. NBS, D67 (1963), 303 | Zbl

[6] E. A. Novikov, ZhETF, 47 (1964), 1919

[7] V. I. Klyatskin, V. I. Tatarskii, TMF, 17 (1973), 273

[8] V. I. Klyatskin, V. I. Tatarskii, UFN, 1973, 499 | DOI

[9] V. I. Klyatskin, V. I. Tatarskii, Izv. VUZov, radiofizika, 14 (1971), 706

[10] O. V. Muzychuk, TMF, 28 (1976), 371