**by
P. J. Fitzsimmons and
Jim Pitman
**

**May 29, 1998**

Mark Kac
introduced a method for
calculating the distribution
of the integral
for a function *v*
of a Markov process and a suitable random time *T*,
which yields the Feynman-Kac formula for the moment-generating
function of .
We review Kac's method, with emphasis on
an aspect often overlooked.
This is Kac's formula for moments of , which may
be stated as follows.
For any random time *T* such that the killed process
is Markov with substochastic semi-group
,
any non-negative measurable function *v*,
and any initial distribution , the moment of
is where
is the Green's operator of the killed process,
is the operator of multiplication by *v*,
and is the function that is identically 1.

- Introduction
- Proof of Kac's Moment Formula
- Corollaries of Kac's Moment Formula
- The Feynman-Kac formula
- Application to Markov Chains
- Application to Local Times
- References
- About this document ...

Wed May 17 08:50:36 PDT 2000