Relations between Stochastic and Partial Differential Equations in Hilbert Spaces

I. V. Melnikova and V. S. Parfenenkova

International Journal of Stochastic Analysis, 2012, vol. 2012, 1-9

Abstract:

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:858736

DOI: 10.1155/2012/858736

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