|
Teoriya Veroyatnostei i ee Primeneniya, 1961, Volume 6, Issue 2, Pages 234–242
(Mi tvp4773)
|
|
|
|
This article is cited in 9 scientific papers (total in 9 papers)
Short Communications
Estimating the Probability Density for Random Processes in Systems
with Nonlinear Reformers of the Piecing-linear Type
È. M. Khazen Moscow
Abstract:
A system of stochastic Ito differential equations is dealt with in this paper: $$dy_i=F(y_1,\dots,y_n ,t)\,dt+\sum\limits_{j=1}^n{a_{ij}\,d\zeta_j (t),}$$ $i=1,2,\dots n$, where ${\zeta_j (t)}$ are independent Wiener processes; or, $$\frac{dy_i }{dt}=F_i(y_1,\dots,y_n ,t)+\sum\limits_{j=1}^n{a_{ij}\zeta_j(t),}$$ where
${\zeta_j (t)}$ are Gaussian “white noise” processes. The functions $F_i(y_1,\dots,y_n )$ are piecewise-linear, and $a_{ij}$ are piecewise-constant.
The problem of estimating the probability density for Markov random processes $(y_1(t),\dots,y_n (t))$ is reduced to the solution of a system of Volterra linear integral equations of second kind.
Received: 20.10.1960
Citation:
È. M. Khazen, “Estimating the Probability Density for Random Processes in Systems
with Nonlinear Reformers of the Piecing-linear Type”, Teor. Veroyatnost. i Primenen., 6:2 (1961), 234–242; Theory Probab. Appl., 6:2 (1961), 214–220
Linking options:
https://www.mathnet.ru/eng/tvp4773 https://www.mathnet.ru/eng/tvp/v6/i2/p234
|
Statistics & downloads: |
Abstract page: | 159 | Full-text PDF : | 225 |
|