Sufficient Conditions for an Operator-Valued Feynman-Kac Formula

Authors

Michael D. Grady, Loyola Marymount UniversityFollow

Document Type

Article

Publication Date

1976

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, ∂u/∂t,=Au + V(x) * u, u(0) = f, where A is the infinitesimal generator of the process X on a certain Banach space and for each x ∈ E, V(x) is the infinitesimal generator of a C₀ contraction semigroup on another Banach space.

Original Publication Citation

Grady, M. D. Sufficient Conditions for an Operator-Valued Feynman-Kac Formula, Transactions of the American Mathematical Society. vol. 223 (1976) pp. 181-203.

Publisher Statement

First published in Transactions of the American Mathematical Society in 1976, published by the American Mathematical Society

Digital Commons @ LMU & LLS Citation

Grady, Michael D., "Sufficient Conditions for an Operator-Valued Feynman-Kac Formula" (1976). Mathematics, Statistics and Data Science Faculty Works. 11.
https://digitalcommons.lmu.edu/math_fac/11