Linear equations and stochastic exponents in a Hilbert space

Authors:
Yuliya Mishura and Georgiy Shevchenko

Translated by:
G. Shevchenko

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **71** (2004).

Journal:
Theor. Probability and Math. Statist. **71** (2005), 139-149

MSC (2000):
Primary 60H10; Secondary 34G10, 47A50, 47D06

Published electronically:
December 30, 2005

MathSciNet review:
2144327

Full-text PDF Free Access

Abstract | References | Similar Articles | 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.

**1.**Wilfried Grecksch and Constantin Tudor,*Stochastic evolution equations*, Mathematical Research, vol. 85, Akademie-Verlag, Berlin, 1995. A Hilbert space approach. MR**1353910****2.**Peter Kotelenez,*A submartingale type inequality with applications to stochastic evolution equations*, Stochastics**8**(1982/83), no. 2, 139–151. MR**686575**, 10.1080/17442508208833233**3.**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****4.**Kôsaku Yosida,*Functional analysis*, 4th ed., Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 123. MR**0350358****5.**A. Pazy,*Semigroups of linear operators and applications to partial differential equations*, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR**710486****6.**Hiroki Tanabe,*Equations of evolution*, Monographs and Studies in Mathematics, vol. 6, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979. Translated from the Japanese by N. Mugibayashi and H. Haneda. MR**533824**

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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

DOI:
http://dx.doi.org/10.1090/S0094-9000-05-00654-X

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