Geodesic
Asymptotic moment stability of solutions to systems of nonlinear differential Itô equations with aftereffect
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2024), pp. 63-76 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper studies the global moment stability of systems of nonlinear Itô differential equations with delays. The analysis is done by a modified regularization method, known as the $W$-method, and based on the use of some auxiliary equation with subsequent application of the theory of positively invertible matrices. Sufficient conditions for the global asymptotic moment stability for both sufficiently general and specific systems of Itô equations formulated in terms of parameters of these systems are given. Connections between this stability and the properties of the delay functions are established.
Keywords: system of stochastic differential equations, nonlinear Itô equation, stability of solutions, asymptotics of solutions, method of auxiliary equations, positive invertibility of matrices. 
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     title = {Asymptotic moment stability of solutions to systems of nonlinear differential {It\^o} equations with aftereffect},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
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}
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R. I. Kadiev; A. V. Ponosov. Asymptotic moment stability of solutions to systems of nonlinear differential Itô equations with aftereffect. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2024), pp. 63-76. http://geodesic.mathdoc.fr/item/IVM_2024_7_a5/

[1] Kolmanovskii V.B., Nosov V.R., Ustoichivost i periodicheskie rezhimy reguliruemykh sistem s posledeistviem, Nauka, M., 1981 | MR

[2] Tsarkov E.F., Sluchainye vozmuscheniya differentsionalno–funktsionalnykh uravnenii, Zinatne, Riga, 1989

[3] Mao X., Stochastic differential equations and applications, Horwood Publ. Ltd., Chichester, 1997 | MR | Zbl

[4] Mohammed S.-E.F., “Stochastic Functional Differential Equations With Memory. Theory, Examples and Applications”, Proc. The Sixth Workshop on Stochastic Anal., Geilo, Norway, 1996, 1–91 | MR

[5] Azbelev N.V., Simonov P.M., Stability of differential equations with aftereffect, Taylor Francis, London, 2003 | MR | Zbl

[6] Azbelev N.V., Maksimov V.P., Rakhmatullina L.F., Introduction to the theory of functional differential equations: methods and applications, Hindawi, New York, 2007 | MR | Zbl

[7] Kadiev R.I., Ponosov A.V., “Globalnaya ustoichivost sistem nelineinykh differentsialnykh uravnenii Ito s posledeistviem i $W$-metod N.V. Azbeleva”, Izv. vuzov. Matem., 2022, no. 1, 38–56 | Zbl

[8] Kadiev R., Ponosov A., “Lyapunov stability of the generalized stochastic pantograph equation”, J. Math., 2018, 7490936, 1–10 | DOI | MR

[9] Kadiev R.I., “Suschestvovanie i edinstvennost resheniya zadachi Koshi dlya funktsionalno–differentsialnykh uravnenii po semimartingalu”, Izv. vuzov. Matem., 1995, no. 10, 35–39 | Zbl

[10] Bellman R., Vvedenie v teoriyu matrits, Nauka, M., 1969

[11] Kadiev R.I., Ustoichivost reshenii stokhasticheskikh funktsionalno-differentsialnykh uravnenii, Disc. \ldots d-ra fiz.-matem. nauk, Makhachkala, 2000