Regularized and generalized solutions of infinite-dimensional stochastic problems / Alshanskiy M. A.,Melnikova I. V. // SBORNIK MATHEMATICS. - 2011. - V. 202, l. 11. - P. 1565-1592.

ISSN/EISSN:

1064-5616 / 1468-4802

Type:

Article

Abstract:

The paper is concerned with solutions of Cauchy's problem for stochastic differential-operator equations in separable Hilbert spaces. Special emphasis is placed on the case when the operator coefficient of the equation is not a generator of a C-0-class semigroup, but rather generates some regularized semigroup. Regularized solutions of equations in the Ito form with a Wiener process as an inhomogeneity and generalized solutions of equations with white noise are constructed in various spaces of abstract distributions.

Author keywords:

regularized semigroup of operators; abstract distribution; generalized solution; Wiener process; white noise STRUCTURE THEOREMS; SEMIGROUPS

DOI:

10.1070/SM2011v202n11ABEH00419

Web of Science ID:

ISI:000299322800001

Соавторы в МНС:

Другие поля

Поле	Значение
Publisher	TURPION LTD
Address	C/O TURPION LTD, IOP PUBLISHING, TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6HG, ENGLAND
Language	English
EISSN	1468-4802
Keywords-Plus	STRUCTURE THEOREMS; SEMIGROUPS
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics
Author-Email	mxa2@yandex.ru Irina.Melnikova@usu.ru
ResearcherID-Numbers	Alshanskiy, Maxim/C-1381-2013
Funding-Acknowledgement	Russian Foundation for Basic Research {[}10-01-96003p]; Ministry of Higher Education and Science of the Russian Federation {[}2.1.1/14118]
Funding-Text	This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 10-01-96003p) and the programme of the Ministry of Higher Education and Science of the Russian Federation (grant no. 2.1.1/14118).
Number-of-Cited-References	23
Usage-Count-Last-180-days	2
Usage-Count-Since-2013	25
Journal-ISO	Sb. Math.
Doc-Delivery-Number	879IL