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.
First published in Transactions of the American Mathematical Society in 1976, published by the American Mathematical Society
Grady, Michael D., "Sufficient Conditions for an Operator-Valued Feynman-Kac Formula" (1976). Mathematics Faculty Works. Paper 11.
Grady, M. D. Sufficient Conditions for an Operator-Valued Feynman-Kac Formula, Transactions of the American Mathematical Society. vol. 223 (1976) pp. 181-203.