Random potentials for Markov processes

The paper is devoted to the integral functionals $\int_0^\infty f(X_t)\,{\mathrm{d}t}$ of Markov processes in $\X$ in the case $d\ge 3$. It is established that such functionals can be presented as the integrals $\int_{\X} f(y) \G(x, \mathrm{d}y, ω)$ with vector valued random measure $\G(x, \mathrm{d}y, ω)$. Some examples such as compound Poisson processes, Brownian motion and diffusions are considered.

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