Relations between Stochastic and Partial Differential Equations in Hilbert Spaces | Zendy

I. V. Melnikova | Zendy; Valentina S. Parfenenkova | Zendy

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Relations between Stochastic and Partial Differential Equations in Hilbert Spaces

Author(s) -

I. V. Melnikova,

Valentina S. Parfenenkova

Publication year - 2012

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.19

H-Index - 28

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/2012/858736

Subject(s) - mathematics , hilbert space , stochastic partial differential equation , generalization , connection (principal bundle) , stochastic differential equation , rigged hilbert space , interpretation (philosophy) , mathematical analysis , hilbert manifold , partial differential equation , pure mathematics , differential equation , reproducing kernel hilbert space , geometry , computer science , programming language

The aim of the paper is to introduce a generalization of the Feynman-Kac theorem in Hilbert spaces. Connection between solutions to the abstract stochastic differential equation and solutions to the deterministic partial differential (with derivatives in Hilbert spaces) equation for the probability characteristic is proved. Interpretation of objects in the equations is given

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