Corrections to the diffusion approximation in stochastic differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 2, pp. 211-223
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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.
@article{TMF_1978_35_2_a6,
author = {S. E. Pitovranov and V. N. Chetverikov},
title = {Corrections to the diffusion approximation in stochastic differential equations},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {211--223},
year = {1978},
volume = {35},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1978_35_2_a6/}
}
TY - JOUR AU - S. E. Pitovranov AU - V. N. Chetverikov TI - Corrections to the diffusion approximation in stochastic differential equations JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1978 SP - 211 EP - 223 VL - 35 IS - 2 UR - http://geodesic.mathdoc.fr/item/TMF_1978_35_2_a6/ LA - ru ID - TMF_1978_35_2_a6 ER -
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/
[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