most recent 30 from http://mathoverflow.net 2013-06-20T02:54:26Z http://mathoverflow.net/feeds/question/88829 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/88829/additive-functional-of-markov-process John Young 2012-02-18T13:39:18Z 2012-02-18T17:30:51Z

<p>I was wondering if there is a way to figure out an explicit formula for the conditional expectation of some Markov additive functional as the following: $$ E_{p}(\exp{[-\int_{0}^{t}g(X_{s})ds]}|X_{t}=q), $$ where $X_{t}$ is a diffusion process, and suppose we have an explicit transition density function of $X_{t}$. Probably Brownian motion is a perfect example for this question, but can we find an explicit formula of the above form?</p>