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Linear equations and stochastic exponents in a Hilbert space
Author(s):
Yuliya
Mishura;
Georgiy
Shevchenko
Translated by:
G. Shevchenko
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 71
(2004).
Journal:
Theor. Probability and Math. Statist.
No. 71
(2005),
139-149.
MSC (2000):
Primary 60H10;
Secondary 34G10, 47A50, 47D06
Posted:
December 30, 2005
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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:
-
- 1.
- W. Greksch and C. Tudor, Stochastic Evolution Equations: A Hilbert Space Approach, Mathematical Research, vol. 85, Akademie Verlag, 1995. MR 1353910 (96m:60130)
- 2.
- P. Kotelenez, A submartingale type inequality with application to stochastic evolution equations, Stochastics 8 (1982), no. 2, 139-152. MR 0686575 (84h:60115)
- 3.
- 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)
- 4.
- K. Yosida, Functional Analysis, Springer-Verlag, Berlin-New York, 1971. MR 0350358 (50:2851)
- 5.
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, Berlin-Heidelberg-NewYork, 1983. MR 0710486 (85g:47061)
- 6.
- 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
DOI:
10.1090/S0094-9000-05-00654-X
PII:
S 0094-9000(05)00654-X
Keywords:
Linear stochastic differential equation,
stochastic exponent
Received by editor(s):
18/DEC/2002
Posted:
December 30, 2005
Additional Notes:
The second author is partially supported by INTAS grant YSF 03-55-2447.
Copyright of article:
Copyright
2005,
American Mathematical Society
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