Geodesic
On the stochastic systems of differential-algebraic type
Journal of computational and engineering mathematics, Tome 1 (2014) no. 1, pp. 34-45.

Voir la notice de l'article provenant de la source Math-Net.Ru

Under the stochastic system of differential-algebraic type we understand the special class of stochastic differential equations in the Ito form, in which in the left - and right-hand sides there are time-dependent continuous rectangular real matrices of the same size, and, in the case of a square matrix, the matrix in the left-hand side is degenerated. In addition, in the right-hand side there is a term that depends only on time. This class of equations is a natural generalization of the class of ordinary differential-algebraic equations. It is assumed that the initial conditions for this class of equations are solutions of some systems of linear algebraic equations, matrices in which are constant and have the same size as in the stochastic system. For the study of this class of equations, we use the machinery that is a generalization of the methods suggested for the study of ordinary differential-algebraic equations in the works by Yu. E. Boyarintsev, V. F. Chistyakov and others. Note that for investigation of these equations we do not use derivative of the right-hand side. We give the necessary information from the theory of pseudo-inverse matrix, and then thransform the system to a form more convenient for study. The result of the article is the statemants, in which sufficient conditions for the existence of solutions are obtained and formulae for finding the solutions are given.
Keywords: differential-algebraic system, Wiener process. 
@article{JCEM_2014_1_1_a3,
     author = {E. Yu. Mashkov},
     title = {On the stochastic systems of differential-algebraic type},
     journal = {Journal of computational and engineering mathematics},
     pages = {34--45},
     publisher = {mathdoc},
     volume = {1},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2014_1_1_a3/}
}
TY  - JOUR
AU  - E. Yu. Mashkov
TI  - On the stochastic systems of differential-algebraic type
JO  - Journal of computational and engineering mathematics
PY  - 2014
SP  - 34
EP  - 45
VL  - 1
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCEM_2014_1_1_a3/
LA  - en
ID  - JCEM_2014_1_1_a3
ER  - 
%0 Journal Article
%A E. Yu. Mashkov
%T On the stochastic systems of differential-algebraic type
%J Journal of computational and engineering mathematics
%D 2014
%P 34-45
%V 1
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCEM_2014_1_1_a3/
%G en
%F JCEM_2014_1_1_a3
E. Yu. Mashkov. On the stochastic systems of differential-algebraic type. Journal of computational and engineering mathematics, Tome 1 (2014) no. 1, pp. 34-45. http://geodesic.mathdoc.fr/item/JCEM_2014_1_1_a3/

[1] Yu. E. Boyarintsev, V. F. Chistyakov, Differentsialno-algebraicheskie sistemy. Medoty resheniya i issledovaniya, Nauka, Novosibirsk, 1998, 224 pp. | MR

[2] V. F. Chistyakov, A. A. Scheglova, Izbrannye glavy teorii algebro-differentsialnykh sistem, Nauka, Novosibirsk, 2003, 319 pp. | MR

[3] B. Oksendal, Stochastic Differential Equations. An Introduction with Applications, Springer, Berlin, 2003 | DOI | MR | Zbl

[4] Yu. E. Gliklikh, Global and Stochastic Analysis with Applications to Mathematical Physics, Springer, London, 2011 | DOI | MR | Zbl

[5] F. R. Gantmakher, Teoriya matrits, Nauka, Moskva, 1966, 576 pp. | MR

[6] Yu. E. Boyarintsev, Regulyarnye i singulyarnye sistemy lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, Novosibirsk, 1980, 224 pp. | MR

[7] Yu. E. Boyarintsev, Metody resheniya vyrozhdennykh sistem obyknovennykh differentsialnykh uravnenii, Nauka, Novosibirsk, 1988, 160 pp. | MR

[8] Yu. E. Boyarintsev, Methods of Solving Singular Systems of Ordinary Differential Equations, Wiley John and Sons, Chichester, 1992, vi+163 pp. | MR | Zbl