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Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2016, Volume 8, Issue 4, Pages 26–32 (Mi vyurm315)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

On the stochastic Leontief type equations with variable matrices given in terms of current velocities of the solution

E. Yu. Mashkov

Southwest State University, Kursk, Russian Federation

Abstract: The stochastic Leontief type equations are a particular case of stochastic systems of differential-algebraic type. The paper deals with the study of the system given in terms of current velocities (symmetric derivatives at an average value) of the solution. It should be noted that in a physical meaning the current velocity of stochastic processes is a direct analog of the physical velocity of deterministic process. The authors assume that the matrices of the system under consideration are rectangular time dependants and satisfy the conditions, under which the system is not solvable with respect to the symmetric derivative. In order to investigate the system of equations the authors use an approach based on the transformation of a square matrix to the canonical Jordan form and changing the metric in the space. The theorem on solution existence for stochastic Leontief type equation with current velocities under some additional conditions on its matrices of coefficients and free terms is proved.

Keywords: derivative at an average value, current velocity, Wiener process, stochastic Leontief type equation.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-00620_а


DOI: https://doi.org/10.14529/mmph160403

Full text: PDF file (235 kB)
References: PDF file   HTML file

UDC: 517.9; 519.216.2
Received: 04.08.2016

Citation: E. Yu. Mashkov, “On the stochastic Leontief type equations with variable matrices given in terms of current velocities of the solution”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 8:4 (2016), 26–32

Citation in format AMSBIB
\Bibitem{Mas16}
\by E.~Yu.~Mashkov
\paper On the stochastic Leontief type equations with variable matrices given in terms of current velocities of the solution
\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.
\yr 2016
\vol 8
\issue 4
\pages 26--32
\mathnet{http://mi.mathnet.ru/vyurm315}
\crossref{https://doi.org/10.14529/mmph160403}
\elib{http://elibrary.ru/item.asp?id=27157548}


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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. E. Yu. Mashkov, D. N. Tyutyunov, “Singulyarnye stokhasticheskie uravneniya leontevskogo tipa v terminakh tekuschikh skorostei resheniya”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:1 (2019), 55–65  mathnet  crossref  elib
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