Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60J35

Retrieve articles in all journals with MSC: 60J35


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

American Mathematical Society