Two Approaches to Infinite Dimensional Extension of Feynman-Kac Theorem / Melnikova Irina V.,Parfenenkova Valentina S. // . - 2015. - V. 113, l. . - P. 225-233.

ISSN/EISSN:

2194-1009 / нет данных

Type:

Proceedings Paper

Abstract:

The relationship between solutions to the abstract Cauchy problem with the generator of a strongly continuous semigroup for the stochastic equation in Hilbert spaces H, H with an H-valued Q-Wiener process W: dX(t) = AX(t)dt + BdW(t), t is an element of{[}0, T], B is an element of L(H, H) and solutions to the infinite dimensional deterministic Cauchy problem partial derivative g/partial derivative t (t, x) = partial derivative g/partial derivative x (t, x)Ax + 1/2Tr {[}B{*}partial derivative(2)g/partial derivative x(2)(t, x)BQ], t is an element of{[}0, T], g(0, x) = h(x) for the probability characteristic g(t, x) = E-0,E-x {[}h(X(t))] with a measurable h : H -> R is under consideration. The main point of the paper is studying the relationship on the basis of two different approaches - ``semigroup approach{''} and ``Ito approach{''}. Special attention is given to the definition and interpretation of objects in the equations.

Author keywords:

нет данных

DOI:

10.1007/978-3-319-12145-1\_14

Web of Science ID:

ISI:000364987300014

Соавторы в МНС:

—

Другие поля

Поле	Значение
Editor	Banasiak, J and Bobrowski, A and Lachowicz, M
Booktitle	SEMIGROUPS OF OPERATORS - THEORY AND APPLICATIONS
Series	Springer Proceedings in Mathematics \& Statistics
Note	Conference on Semigroups of Operators - Theory and Applications, Bedlewo, POLAND, OCT, 2013
Organization	Int Banach Ctr; Polish Acad Sci, Math Inst; Lublin Univ Technol; Lodz Univ Technol; Univ Warsaw; Natl Res Fdn S Africa
Publisher	SPRINGER
Address	233 SPRING STREET, NEW YORK, NY 10013, UNITED STATES
Language	English
ISBN	978-3-319-12145-1; 978-3-319-12144-4
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics; Statistics \& Probability
Author-Email	Irina.Melnikova@usu.ru vika8887@e1.ru
Number-of-Cited-References	8
Doc-Delivery-Number	BD9NB