Relations between stochastic and partial differential equations in Hilbert spaces (Q1929685)
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scientific article; zbMATH DE number 6123599
| Language | Label | Description | Also known as |
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| English | Relations between stochastic and partial differential equations in Hilbert spaces |
scientific article; zbMATH DE number 6123599 |
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Relations between stochastic and partial differential equations in Hilbert spaces (English)
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9 January 2013
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Summary: 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 \(dX(t) = AX(t)dt + BdW(t)\) and solutions to the deterministic partial differential (with derivatives in Hilbert spaces) equation for the probability characteristic \(\operatorname{E}^{t, x}h(X(T))\) is proved. Interpretation of objects in the equations is given.
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Feynman-Kac theorem
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Hilbert spaces
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stochastic differential equation
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