Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process

P. J. Fitzsimmons and Jim Pitman

Stochastic Processes and their Applications, 1999, vol. 79, issue 1, 117-134

Abstract: Mark Kac introduced a method for calculating the distribution of the integral Av=[integral operator]0Tv(Xt) dt for a function v of a Markov process (Xt, t[greater-or-equal, slanted]0) and a suitable random time T, which yields the Feynman-Kac formula for the moment-generating function of Av. We review Kac's method, with emphasis on an aspect often overlooked. This is Kac's formula for moments of Av, which may be stated as follows. For any random time T such that the killed process (Xt, 0[less-than-or-equals, slant]t

Keywords: Occupation; time; Local; time; Resolvent; Killed; process; Terminal; time; Green's; operator (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (8)

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