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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, Issue 13, Pages 24–34 (Mi vyuru65)  

This article is cited in 6 scientific papers (total in 6 papers)

Mathematical Modelling

Investigation of Leontieff Type Equations with White Noise by the Methods of Mean Derivatives of Stochastic Processes

Yu. E. Gliklikh

Voronezh State University (Voronezh, Russian Federation)

Abstract: We understand the Leontieff type equation with white noise as the expression of the form $L\dot\xi(t)=M\xi(t)+\dot w(t)$ where $L$ is a degenerate matrix $n\times n$, $M$ is a non-degenerate matrix $n\times n$, $\xi(t)$ is a stochastic process we are looking for and $\dot w(t)$ is the white noise. Since the derivative $\dot\xi(t)$ and the white noise are well-posed only in terms of distributions, the direct investigation of such equations is very complicated. We involve two methods in the investigation. First, we pass to the stochastic differential equation $L\xi(t)=M\int_0^t\xi(s)ds+w(t)$, where $w(t)$ is Wiener process, and then for describing solutions of this equations we apply the so called Nelson mean derivatives that are introduced without using the distributions. By these methods we obtain formulae for solutions of Leotieff type equations with white noise.

Keywords: mean derivative, current velocity, white nose, Wiener process, Leontieff type equation.

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Document Type: Article
UDC: 517.9+519.216.2
MSC: 60H30
Received: 31.05.2012

Citation: Yu. E. Gliklikh, “Investigation of Leontieff Type Equations with White Noise by the Methods of Mean Derivatives of Stochastic Processes”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, no. 13, 24–34

Citation in format AMSBIB
\Bibitem{Gli12}
\by Yu.~E.~Gliklikh
\paper Investigation of Leontieff Type Equations with White Noise by the Methods of Mean Derivatives of Stochastic Processes
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2012
\issue 13
\pages 24--34
\mathnet{http://mi.mathnet.ru/vyuru65}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. E. Gliklikh, E. Yu. Mashkov, “Stochastic Leontieff type equations and mean derivatives of stochastic processes”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 6:2 (2013), 25–39  mathnet
    2. G. A. Sviridyuk, N. A. Manakova, “Dinamicheskie modeli sobolevskogo tipa s usloviem Shouoltera–Sidorova i additivnymi «shumami»”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 7:1 (2014), 90–103  mathnet  crossref
    3. A. A. Zamyshlyaeva, “One nonclassical higher order mathematical model with additive ‘`white noise"’”, J. Comp. Eng. Math., 1:1 (2014), 55–68  mathnet  zmath  elib
    4. A. L. Shestakov, A. V. Keller, G. A. Sviridyuk, “The theory of optimal measurements”, J. Comp. Eng. Math., 1:1 (2014), 3–16  mathnet  zmath  elib
    5. A. V. Keller, “On the computational efficiency of the algorithm of the numerical solution of optimal control problems for models of Leontieff type”, J. Comp. Eng. Math., 2:2 (2015), 39–59  mathnet  crossref  elib
    6. Yu. E. Gliklikh, E. Yu. Mashkov, “Stochastic Leontieff type equations in terms of current velocities of the solution II”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:3 (2016), 31–40  mathnet  crossref  elib
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