Geodesic
Statistical averages in dynamical systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 17 (1973) no. 2, pp. 273-282

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

General formulas are deduced for calculating the correlation of a random process with a functional over it. These formulas yield closed equations for the probability densities of dynamical systems with random parameters. Parametric resonance in a system whose eigenfrequency is a random function of the time is considered as an example. An equation of general form is obtained for the joint probability density of the coordinate and velocity, this going over into the Einstein–Fokker equation if the frequency is a Gaussian $\delta$-correlated function of the time and into the Kolmogorov–Feller equation if the frequency is a generalized Poisson $\delta$-correlated random process. 
@article{TMF_1973_17_2_a14,
     author = {V. I. Klyatskin and V. I. Tatarskii},
     title = {Statistical averages in dynamical systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {273--282},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_17_2_a14/}
}
TY  - JOUR
AU  - V. I. Klyatskin
AU  - V. I. Tatarskii
TI  - Statistical averages in dynamical systems
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1973
SP  - 273
EP  - 282
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1973_17_2_a14/
LA  - ru
ID  - TMF_1973_17_2_a14
ER  - 
%0 Journal Article
%A V. I. Klyatskin
%A V. I. Tatarskii
%T Statistical averages in dynamical systems
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1973
%P 273-282
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1973_17_2_a14/
%G ru
%F TMF_1973_17_2_a14
V. I. Klyatskin; V. I. Tatarskii. Statistical averages in dynamical systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 17 (1973) no. 2, pp. 273-282. http://geodesic.mathdoc.fr/item/TMF_1973_17_2_a14/