Evolution of a simple dynamical system in a random field
Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 3, pp. 414-419 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The solution of the Fokker–Planck equation for a nonlinear dynamical system is considered in the framework of perturbation theory. On the basis of uniform estimates, we find a condition for the applicability of the Gaussian approximation of solutions in the neighborhood of an asymptotically stable point of a deterministic system.
@article{TMF_1993_97_3_a7,
     author = {M. Kh. Kharrasov},
     title = {Evolution of a~simple dynamical system in a~random field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {414--419},
     year = {1993},
     volume = {97},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_97_3_a7/}
}
TY  - JOUR
AU  - M. Kh. Kharrasov
TI  - Evolution of a simple dynamical system in a random field
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1993
SP  - 414
EP  - 419
VL  - 97
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1993_97_3_a7/
LA  - ru
ID  - TMF_1993_97_3_a7
ER  - 
%0 Journal Article
%A M. Kh. Kharrasov
%T Evolution of a simple dynamical system in a random field
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1993
%P 414-419
%V 97
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1993_97_3_a7/
%G ru
%F TMF_1993_97_3_a7
M. Kh. Kharrasov. Evolution of a simple dynamical system in a random field. Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 3, pp. 414-419. http://geodesic.mathdoc.fr/item/TMF_1993_97_3_a7/

[1] Bogolyubov N. N., On the Stochastic processes in the Dynamical Systems, preprint E17-10514, JINR, Dubna, 1977; ФЭЧАЯ, 9:4 (1978), 501–579 | MR

[2] Prigogine I., Nonequilibrium Statistical Mechanics, Wiley, N. Y., 1962 | MR | Zbl

[3] Van Kampen N. G., Stochastic Processes in Physics and Chemistry, North Holland, Amsterdam, 1981 | MR | Zbl

[4] Ito K., Veroyatnostnye protsessy, vyp. 2, IL, M., 1963 | MR

[5] Onsager L., Machlup S., Phys. Rev., 91:6 (1953), 1505–1512 | DOI | MR | Zbl

[6] Machlup S., Onsager L., Phys. Rev., 91:6 (1953), 1512–1515 | DOI | MR | Zbl

[7] Goel N. S., Maitra S. C., Montroll E. W., Rev. Mod. Phys., 43:2 (1971), 231–276 | DOI | MR

[8] Keizer J., J. Chem. Phys., 63:1 (1975), 398–403 ; 64:4 (1976), 1679–1687 | DOI | DOI | MR

[9] Ottinger H. C., J. Chem. Phys., 90:1 (1989), 463–473 | DOI

[10] Graham R., “Stochastic Methods in Nonequilibrium Thermodynamics”, Stochastic Nonlinear Systems in Physics, Chemistry and Biology, Springer, Berlin, Heidelberg, N. Y., 1981 | Zbl

[11] Alekseev V. V., Kharrasov M. Kh., TMF, 88:1 (1991), 96–103 | MR

[12] Kharrasov M. Kh., DAN SSSR, 325:2 (1992), 280–283 | MR | Zbl