Geodesic
Studies of stability problems for linear stochastic functional-differential equations by N.\,V.~Azbelev’s $W$-method>>
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 39 (2012) no. 1, pp. 64-65.

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

N. V. Azbelev’s ideas, which have been developed in connections with the studies of stability of solutions to linear stochastic functional differential equations, are briefly summarized.
Keywords: stability of solutions, method of the auxiliary equations. 
@article{IIMI_2012_39_1_a27,
     author = {R. I. Kadiev and A. V. Ponosov},
     title = {Studies of stability problems for linear stochastic functional-differential equations by {N.\,V.~Azbelev{\textquoteright}s} <<$W$-method>>},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {64--65},
     publisher = {mathdoc},
     volume = {39},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a27/}
}
TY  - JOUR
AU  - R. I. Kadiev
AU  - A. V. Ponosov
TI  - Studies of stability problems for linear stochastic functional-differential equations by N.\,V.~Azbelev’s <<$W$-method>>
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2012
SP  - 64
EP  - 65
VL  - 39
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a27/
LA  - ru
ID  - IIMI_2012_39_1_a27
ER  - 
%0 Journal Article
%A R. I. Kadiev
%A A. V. Ponosov
%T Studies of stability problems for linear stochastic functional-differential equations by N.\,V.~Azbelev’s <<$W$-method>>
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2012
%P 64-65
%V 39
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a27/
%G ru
%F IIMI_2012_39_1_a27
R. I. Kadiev; A. V. Ponosov. Studies of stability problems for linear stochastic functional-differential equations by N.\,V.~Azbelev’s <<$W$-method>>. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 39 (2012) no. 1, pp. 64-65. http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a27/

[1] Azbelev N.V., Maksimov V.P., Rakhmatullina L.F., Vvedenie v teoriyu funktsionalno-differentsialnykh uravnenii, Nauka, M., 1991 \, 280 pp.

[2] Barbashin E.A., Vvedenie v teoriyu ustoichivosti, Nauka, M., 1967, 224 pp.

[3] Berezanskii L.M., “Razvitie $W$-metoda N. V. Azbeleva v zadachakh ustoichivosti reshenii lineinykh funktsionalno-differentsialnykh uravnenii”, Differentsialnye uravneniya, 22:5 (1986), 739–750 | MR | Zbl

[4] Kadiev R.I., Ponosov A.V., “Ustoichivost stokhasticheskikh funktsionalno-differentsialnykh uravnenii pri postoyanno deistvuyuschikh vozmuscheniyakh”, Differentsialnye uravneniya, 28:2 (1992), 198–207 | MR

[5] Kadiev R.I., “Dostatochnye usloviya ustoichivosti stokhasticheskikh sistem s posledeistviem”, Differents. uravneniya, 30:2 (1994), 555–564 | MR | Zbl

[6] Kadiev R.I., Ustoichivost reshenii stokhasticheskikh funktsionalno-differentsialnykh uravnenii, dis. \ldots d-ra fiz.-matem. nauk, IMM UrO RAN, Ekaterinburg, 2000, 231 pp.

[7] Kadiev R.I., Ponosov A., “Relations between stability and admissibility for stochastic linear functional differential equations”, J. Func. Diff. Equations, 2004, 1–28

[8] Kadiev R.I., Ponosov A., “Stability of stochastic functional differential equations and the $W$-transform”, El. J. Diff. Equations, 92 (2004), 1–36 | MR

[9] Kadiev R.I., Ponosov A., “Linear stochastic functional differential equations: stability, admissible pairs of spaces and N. V. Azbelev's $W$-method”, Problems of Nonlin. An. in Engineering Syst., 25:1 (2006), 57–89

[10] Kadiev R.I., Ponosov A., “Stability of solutions of linear impulsive systems of Ito differential equations with aftereffect”, Differential Equtions, 43:7 (2007), 898–904 | DOI | MR | Zbl

[11] Kadiev R.I., Ponosov A., “Stability of solutions of linear impulsive systems of stochastic differential equations with bounded delays”, Differential Equations, 46:3 (2010), 486–498 | MR | Zbl

[12] Kadiev R.I., Ponosov A., “The $W$-transform in stability analysis for stochastic linear functional difference equations”, J. Math. Analysis and Appl., 389:2 (2012), 1239–1250 | DOI | MR | Zbl

[13] Kadiev R.I., Ponosov A., “Stability of Impulsive Stochastic Differential Equations with Linear Delays”, J. of Abstract Diff. Equations and Appl., 2:2 (2012), 7–25 | MR

[14] Kolmanovskii V.B., Nosov V.R., Stability of Functional Differential Equations, Academic Press, New York, 1986, 217 pp. | MR | Zbl

[15] Mao X., Stochastic Differential Equations and Applications, Horwood Publishing ltd., Chichester, 1997, 360 pp. | MR | Zbl