On the properties of the second moment of solutions of stochastic differentialfunctional equations with varying coefficients
Authors:
V. K. Yasins'kii and S. V. Antonyuk
Translated by:
V. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 70 (2004).
Journal:
Theor. Probability and Math. Statist. 70 (2005), 177184
MSC (2000):
Primary 60F15, 60G42; Secondary 62H12, 62J05
Published electronically:
August 12, 2005
MathSciNet review:
2110874
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: Sufficient conditions for the mean square stability of solutions of linear stochastic differentialfunctional ItôSkorokhod equations with unbounded aftereffect are obtained in the paper. The critical case is also studied.
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V. K. Yasins'ki and S. V. Antonyuk, The mean square stability of differentialfunctional equations with the whole history, Proceedings of the Second International Conference on Applied Mathematics APLIMAT (February 57, 2003, Bratislava), Slovak Technical University, Bratislava, 2003, pp. 725732.
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 V. E. Slyusarchuk, E. F. Tsar'kov, and V. K. Yasins'ki, The stability of the solutions of linear differentialfunctional equations under random perturbations of the parameters, Ukrain. Mat. Zh. 25 (1973), no. 3, 412418; English transl. in Ukrainian Math. J. 25 (1974), no. 3, 338343. MR 0331514 (48:9847)
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 V. E. Slyusarchuk and V. K. Yasins'ki, Stability of solutions of stochastic functionaldifferential equations in the critical case, Izv. AN BSSR Ser. fiz.mat. nauk (1977), 109115. (Russian)
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 A. V. Skorokhod, Studies in the Theory of Random Processes, Kiev University, Kiev, 1961; English transl., AddisonWesley Publishing Co. Inc., Reading, Mass., 1965. MR 0185620 (32:3082a); MR 0185620 (32:3082b)
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 V. K. Yasins'ki and S. V. Antonyuk, The mean square stability of differentialfunctional equations with the whole history, Proceedings of the Second International Conference on Applied Mathematics APLIMAT (February 57, 2003, Bratislava), Slovak Technical University, Bratislava, 2003, pp. 725732.
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Additional Information
V. K. Yasins'kii
Affiliation:
Department of Mathematics, Chernivtsi National Yuriy Fedkovich University, Universitets’ka Street 28, Chernivtsi 58012, Ukraine
Email:
yasik@cv.ukrtel.net
S. V. Antonyuk
Affiliation:
Department of Mathematics, Chernivtsi National Yuriy Fedkovich University, Universitets’ka Street 28, Chernivtsi 58012, Ukraine
DOI:
http://dx.doi.org/10.1090/S0094900005006411
PII:
S 00949000(05)006411
Received by editor(s):
April 8, 2003
Published electronically:
August 12, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
