XIV: 39, 347-356, LNM 784 (1980)
CHUNG, Kai Lai
On stopped Feynman-Kac functionals (
Markov processes,
Diffusion theory)
Let $(X_t)$ be a strong Markov process with continuous paths on the line, and let $\tau_b$ be the hitting time of the point $b$. It is assumed that $\tau_b$ is $P_a$-a.s. finite for all $a,b$. The purpose of the paper is to study the quantities $u(a,b)=E_a[\,\exp(\int_0^{\tau_b} q(X_s)\,ds)\,]$ where $q$ is bounded. Then (among other results) if $u(a,b)<\infty$ for all $a<b$, we have $u(a,b)\,u(b,a)\le 1$ for all $a,b$
Keywords: Hitting probabilitiesNature: Original
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