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Teor. Veroyatnost. i Primenen., 1961, Volume 6, Issue 2, Pages 234–242 (Mi tvp4773)  

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:
$$dy_i=F(y_1,…,y_n ,t) dt+\sum\limits_{j=1}^n{a_{ij} d\zeta_j (t),}$$
$i=1,2,…n$, where ${\zeta_j (t)}$ are independent Wiener processes; or,
$$\frac{dy_i }{dt}=F_i(y_1,…,y_n ,t)+\sum\limits_{j=1}^n{a_{ij}\zeta_j(t),}$$
where ${\zeta_j (t)}$ are Gaussian “white noise” processes. The functions $F_i(y_1,…,y_n )$ are piecewise-linear, and $a_{ij}$ are piecewise-constant.
The problem of estimating the probability density for Markov random processes $(y_1(t),…,y_n (t))$ is reduced to the solution of a system of Volterra linear integral equations of second kind.

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English version:
Theory of Probability and its Applications, 1961, 6:2, 214–220

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

Citation in format AMSBIB
\Bibitem{Kha61}
\by \`E.~M.~Khazen
\paper Estimating the Probability Density for Random Processes in Systems
with Nonlinear Reformers of the Piecing-linear Type
\jour Teor. Veroyatnost. i Primenen.
\yr 1961
\vol 6
\issue 2
\pages 234--242
\mathnet{http://mi.mathnet.ru/tvp4773}
\transl
\jour Theory Probab. Appl.
\yr 1961
\vol 6
\issue 2
\pages 214--220
\crossref{https://doi.org/10.1137/1106029}


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