## Sufficient conditions for an operator-valued Feynman-Kac formula

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- by Michael Dale Grady PDF
- Trans. Amer. Math. Soc.
**223**(1976), 181-203 Request permission

## Abstract:

Let*E*be a locally compact, second countable Hausdorff space and let $X(t)$ be a Markov process with state space

*E*. Sufficient conditions are given for the existence of a solution to the initial value problem, $\partial u/\partial t = Au + V(x) \cdot u,u(0) = f$, where

*A*is the infinitesimal generator of the process

*X*on a certain Banach space and for each $x \in E,V(x)$ is the infinitesimal generator of a ${C_0}$ contraction semigroup on another Banach space.

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## Additional Information

- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**223**(1976), 181-203 - MSC: Primary 60J35
- DOI: https://doi.org/10.1090/S0002-9947-1976-0423552-5
- MathSciNet review: 0423552