| Title | ABSTRACT STOCHASTIC PROBLEMS WITH GENERATORS OF REGULARIZED SEMIGROUPS |
| Publication Type | Journal Article |
| Year of Publication | 2009 |
| Authors | MELNIKOVA, IRINAV, FILINKOV, ALEXEI |
| Secondary Title | Communications in Applied Analysis |
| Volume | 13 |
| Issue | 2 |
| Start Page | 195 |
| Pagination | 212 |
| Date Published | 04/2009 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 34F05, 34G10, 46F10, 47D62, 60H10 |
| Abstract | We study the stochastic Cauchy problem
 where A is the generator of a regularized semigroup in a separable Hilbert space H, B is a bounded
linear operator and W is an H-valued Wiener process on a probability space (Ω, F, P ). We construct regularized solutions to this problem in L 2 (Ω; H) and in spaces of abstract stochastic distributions. We also study the semi-linear problem  where F and B satisfy some appropriate growth and Lipschitz conditions.
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| Short Title | ABSTRACT STOCHASTIC PROBLEMS |
| Refereed Designation | Refereed |
| Full Text | REFERENCES[1] A.V.Balakrishnan, Applied functional Analysis, Springer-Verlag, New-York, Heidelberg, 1976.
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