|
Teoriya Veroyatnostei i ee Primeneniya, 1966, Volume 11, Issue 3, Pages 444–462
(Mi tvp640)
|
|
|
|
This article is cited in 467 scientific papers (total in 467 papers)
Предельная теорема для решений дифференциальных уравнений со случайной правой частью
R. Z. Khas'minskii Moscow
Abstract:
The asymptotic behaviour of the solution $X_\varepsilon(t,\omega)$ of equation (0.1) as $\varepsilon\to0$ is considered. The main assumptions are the following ones: 1) condition (1.1) is fulfilled and the processes $F^{(i)}(x,t,\omega)$ satisfy Ibragirnov's mixing condition (1.5) with $T^6\beta(T)\downarrow0$ as $T\to\infty$, 2) limits (1.4) exist and $\overline\Phi^0(x)\equiv0$. The weak convergence of the process $X_\varepsilon(\tau,\omega)$ $(\tau=\varepsilon^2t)$ to a Markov process $X_0(\tau,\omega)$ is proved. Moreover the local characteristics of the process $X_0(\tau,\omega)$ are calculated. An application of this theorem to the problem of parametric excitation of linear systems by random forces is considered
Received: 14.09.1965
Citation:
R. Z. Khas'minskii, “Предельная теорема для решений дифференциальных уравнений со случайной правой частью”, Teor. Veroyatnost. i Primenen., 11:3 (1966), 444–462; Theory Probab. Appl., 11:3 (1966), 390–406
Linking options:
https://www.mathnet.ru/eng/tvp640 https://www.mathnet.ru/eng/tvp/v11/i3/p444
|
|