Geodesic
Global stability of systems of nonlinear It\^{o} differential equations with aftereffect and N.V. Azbelev's $W$-method
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2022), pp. 38-56

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

The work studies the global moment stability of solutions of systems of nonlinear differential Ito equations with delays. A modified regularization method ($W$ -method) for the analysis of various types of stability of such systems, based on the choice of the auxiliary equations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.
Keywords: nonlinear Itô equations, stability of solutions, method of auxiliary equations, positive invertibility of matrices, bounded delays. 
@article{IVM_2022_1_a3,
     author = {R. I. Kadiev and A. V. Ponosov},
     title = {Global stability of systems of nonlinear {It\^{o}} differential equations with aftereffect and {N.V.} {Azbelev's} $W$-method},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {38--56},
     publisher = {mathdoc},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_1_a3/}
}
TY  - JOUR
AU  - R. I. Kadiev
AU  - A. V. Ponosov
TI  - Global stability of systems of nonlinear It\^{o} differential equations with aftereffect and N.V. Azbelev's $W$-method
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2022
SP  - 38
EP  - 56
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2022_1_a3/
LA  - ru
ID  - IVM_2022_1_a3
ER  - 
%0 Journal Article
%A R. I. Kadiev
%A A. V. Ponosov
%T Global stability of systems of nonlinear It\^{o} differential equations with aftereffect and N.V. Azbelev's $W$-method
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2022
%P 38-56
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2022_1_a3/
%G ru
%F IVM_2022_1_a3
R. I. Kadiev; A. V. Ponosov. Global stability of systems of nonlinear It\^{o} differential equations with aftereffect and N.V. Azbelev's $W$-method. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2022), pp. 38-56. http://geodesic.mathdoc.fr/item/IVM_2022_1_a3/