Stochastically bounded solutions of a linear nonhomogeneous stochastic differential equation
Author:
O. V. Il’chenko
Translated by:
V. Semenov
Journal:
Theor. Probability and Math. Statist. 68 (2004), 41-48
MSC (2000):
Primary 60H10; Secondary 34F05
DOI:
https://doi.org/10.1090/S0094-9000-04-00596-4
Published electronically:
May 24, 2004
MathSciNet review:
2000393
Full-text PDF Free Access
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Abstract: Conditions for the existence of a stochastically bounded solution of a linear nonhomogeneous stochastic differential equation are found in the paper. The stationary and periodic cases are considered.
References
- L. Arnold and R. Khasminskiĭ, Stability index for nonlinear stochastic differential equations, Stochastic Analysis (M. Cranston and M. Pinsky, eds.), Proc. Sympos. Pure Math., vol 57, Amer. Math. Soc., Providence, RI, 1995, 543–552. MR 96e:60100
- I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations, “Naukova Dumka”, Kiev, 1968; English transl., Springer-Verlag, Berlin, 1972. MR 41:7777; MR 49:11625
- A. V. Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations, “Naukova Dumka”, Kiev, 1987; English transl., Amer. Math. Soc., Providence, RI, 1989. MR 88m:60164; MR 90i:60038
- N. Ikeda and S. Vatanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981. MR 84b:60080
- Yu. L. Daletskiĭ and M. G. Krein, Stability of Solutions of Differential Equations in Banach Spaces, “Nauka”, Moscow, 1970; English transl., Amer. Math. Soc., Providence, RI, 1974. MR 50:5125
- A. Ya. Dorogovtsev, Periodic and Stationary Regimes of Infinite-Dimensional Deterministic and Stochastic Dynamic Systems, “Vyshcha Shkola”, Kiev, 1992. (Russian) MR 94c:60097
- A. Ichikawa, Bounded and Periodic Solutions of a Linear Stochastic Evolution Equations, Lect. Notes Math., vol. 1299, Springer-Verlag, 1988, 124–130. MR 89f:60061
- R. Z. Khas’minskiĭ, Stability of Systems of Differential Equations under Random Perturbations of Their Parameters, “Nauka”, Moscow, 1969; English transl., Sijthoff & Noordhoff, Alphen aan Rijn, 1980. MR 41:3925; MR 82b:60064
References
- L. Arnold and R. Khasminskiĭ, Stability index for nonlinear stochastic differential equations, Stochastic Analysis (M. Cranston and M. Pinsky, eds.), Proc. Sympos. Pure Math., vol 57, Amer. Math. Soc., Providence, RI, 1995, 543–552. MR 96e:60100
- I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations, “Naukova Dumka”, Kiev, 1968; English transl., Springer-Verlag, Berlin, 1972. MR 41:7777; MR 49:11625
- A. V. Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations, “Naukova Dumka”, Kiev, 1987; English transl., Amer. Math. Soc., Providence, RI, 1989. MR 88m:60164; MR 90i:60038
- N. Ikeda and S. Vatanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981. MR 84b:60080
- Yu. L. Daletskiĭ and M. G. Krein, Stability of Solutions of Differential Equations in Banach Spaces, “Nauka”, Moscow, 1970; English transl., Amer. Math. Soc., Providence, RI, 1974. MR 50:5125
- A. Ya. Dorogovtsev, Periodic and Stationary Regimes of Infinite-Dimensional Deterministic and Stochastic Dynamic Systems, “Vyshcha Shkola”, Kiev, 1992. (Russian) MR 94c:60097
- A. Ichikawa, Bounded and Periodic Solutions of a Linear Stochastic Evolution Equations, Lect. Notes Math., vol. 1299, Springer-Verlag, 1988, 124–130. MR 89f:60061
- R. Z. Khas’minskiĭ, Stability of Systems of Differential Equations under Random Perturbations of Their Parameters, “Nauka”, Moscow, 1969; English transl., Sijthoff & Noordhoff, Alphen aan Rijn, 1980. MR 41:3925; MR 82b:60064
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Additional Information
O. V. Il’chenko
Affiliation:
Department of Mathematics, Mechanics and Mathematics Faculty, Kyiv National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 02022, Ukraine
Email:
avi@univ.kiev.ua
Received by editor(s):
June 17, 2002
Published electronically:
May 24, 2004
Article copyright:
© Copyright 2004
American Mathematical Society
