FEYNMAN-KAC THEOREM IN HILBERT SPACES / Melnikova Irina V.,Parfenenkova Valentina S. // ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS. - 2014. - V. , l. .

ISSN/EISSN:

1072-6691 / нет данных

Type:

Article

Abstract:

In this article we study the relationship between solutions to Cauchy problems for the abstract stochastic differential equation dX(t) = AX(t)dt + BdW(t) and solutions to Cauchy problems (backward and forward) for the infinite dimensional deterministic partial differential equation +/-partial derivative g/partial derivative t(t,x) + partial derivative g/partial derivative x(t,x)Ax +1/2 Tr{[}(BQ(1/2)){*} partial derivative(2)g/partial derivative x(2)(t,x)(BQ(1/2))]= 0, where g is the probability characteristic g - E-t,E-x {[}h(X(T))] in the backward case and g = E-0,E-x{[}h(X(t))] in the forward case. This relationship, that is the inifinite dimensional Feynman-Kac theorem, is proved in both directions: from stochastic to deterministic and from deterministic to stochastic. Special attention is given to the definition and interpretation of objects in the equations.

Author keywords:

Semigroups of operators; infinite dimensional stochastic equations; diffusion processes; Kolmogorov equations

DOI:

нет данных

Web of Science ID:

ISI:000350637700002

Соавторы в МНС:

—

Другие поля

Поле	Значение
Month	OCT 7
Publisher	TEXAS STATE UNIV
Address	601 UNIVERSTITY DRIVE, SAN MARCOS, TX 78666 USA
Language	English
Article-Number	208
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	Irina.Melnikova@usu.ru vika8887@e1.ru
Funding-Acknowledgement	Program for State Support of Leading Universities of the Russian Federation {[}02.A03.21.0006]; RFBR {[}13-01-00090]
Funding-Text	This research was supported by the Program for State Support of Leading Universities of the Russian Federation (agreement no. 02.A03.21.0006 of August 27, 2013) and grant RFBR no. 13-01-00090.
Number-of-Cited-References	16
Journal-ISO	Electron. J. Differ. Equ.
Doc-Delivery-Number	CC8SE