Linear equations and stochastic exponents in a Hilbert space
Authors:
Yuliya Mishura and Georgiy Shevchenko
Translated by:
G. Shevchenko
Journal:
Theor. Probability and Math. Statist. 71 (2005), 139-149
MSC (2000):
Primary 60H10; Secondary 34G10, 47A50, 47D06
DOI:
https://doi.org/10.1090/S0094-9000-05-00654-X
Published electronically:
December 30, 2005
MathSciNet review:
2144327
Full-text PDF Free Access
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Additional Information
Abstract: We consider linear stochastic differential equations in a Hilbert space and obtain general limit theorems. As a corollary, we get a result on the convergence of finite-dimensional approximations of solutions of such equations.
References
- Wilfried Grecksch and Constantin Tudor, Stochastic evolution equations, Mathematical Research, vol. 85, Akademie-Verlag, Berlin, 1995. A Hilbert space approach. MR 1353910
- Peter Kotelenez, A submartingale type inequality with applications to stochastic evolution equations, Stochastics 8 (1982/83), no. 2, 139–151. MR 686575, DOI https://doi.org/10.1080/17442508208833233
- Hiroshi Kunita, On the representation of solutions of stochastic differential equations, Seminar on Probability, XIV (Paris, 1978/1979) Lecture Notes in Math., vol. 784, Springer, Berlin, 1980, pp. 282–304. MR 580134
- Kôsaku Yosida, Functional analysis, 4th ed., Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 123. MR 0350358
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References
- W. Greksch and C. Tudor, Stochastic Evolution Equations: A Hilbert Space Approach, Mathematical Research, vol. 85, Akademie Verlag, 1995. MR 1353910 (96m:60130)
- P. Kotelenez, A submartingale type inequality with application to stochastic evolution equations, Stochastics 8 (1982), no. 2, 139–152. MR 0686575 (84h:60115)
- H. Kunita, On the Representation of Solutions of SDEs, Séminaire de Prob. XIV, Lect. Notes Math., Springer-Verlag, Berlin, 1980, 282–304. MR 0580134 (82e:58028)
- K. Yosida, Functional Analysis, Springer-Verlag, Berlin–New York, 1971. MR 0350358 (50:2851)
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, Berlin–Heidelberg–NewYork, 1983. MR 0710486 (85g:47061)
- H. Tanabe, Equations of Evolution, Pitman, London, 1979. MR 0533824 (82g:47032)
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Additional Information
Yuliya Mishura
Affiliation:
Chair of Probability Theory and Mathematical Statistics, Department of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Glushkov pr. 6, Kyiv 03127,Ukraine
Email:
myus@univ.kiev.ua
Georgiy Shevchenko
Affiliation:
Chair of Probability Theory and Mathematical Statistics, Department of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Glushkov pr. 6, Kyiv 03127,Ukraine
Email:
zhora@univ.kiev.ua
Keywords:
Linear stochastic differential equation,
stochastic exponent
Received by editor(s):
December 18, 2002
Published electronically:
December 30, 2005
Additional Notes:
The second author is partially supported by INTAS grant YSF 03-55-2447.
Article copyright:
© Copyright 2005
American Mathematical Society
