On the Feynman-Kac formula. (English) Zbl 1468.60082
Joshua, V. C. (ed.) et al., Applied probability and stochastic processes. Selected papers based on the presentations at the international conference, Kerala, India, January, 7–10 2019. In honour of Prof. Dr. A. Krishnamoorthy. Singapore: Springer. Infosys Sci. Found. Ser., 491-506 (2020).
Summary: In this article given \(y:[0,\eta)\rightarrow H\), a continuous map into a Hilbert space \(H\), we study the equation
\[
\hat{y}(t)=e^{\int\limits_0^tc(s,\hat{y})ds}y(t),
\]
where \(c(s,\cdot)\) is a given “potential” on \(C([0,\eta),H)\). Applying the transformation \(y\rightarrow\hat{y}\) to the solutions of the SPDE and SDE underlying a diffusion, we study the Feynman-Kac formula.
For the entire collection see [Zbl 1468.60003].
For the entire collection see [Zbl 1468.60003].
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60B11 | Probability theory on linear topological spaces |
Keywords:
\(\mathcal{S}^\prime\) valued process; diffusion processes; Hermite-Sobolev space; path transformations; quasi-linear SPDE; Feynman-Kac formula; translation invarianceReferences:
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