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Sufficient conditions for an operator-valued Feynman-Kac formula


Author: Michael Dale Grady
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
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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

DOI: https://doi.org/10.1090/S0002-9947-1976-0423552-5
Keywords: Function space integrals, semigroups of operators, Markov processes, random evolutions, multiplicative operator functionals
Article copyright: © Copyright 1976 American Mathematical Society

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