Random potentials for Markov processes

The paper is devoted to the integral functionals $\int_0^\infty f(X_t),{$\mathrm{d}$t}$ofMarkovprocessesin$\X$inthecase$d\ge 3$. It is established that such functionals can be presented as the integrals $\int_{\X} f(y) \G(x, $\mathrm{d}$y, \omega)$withvectorvaluedrandommeasure$\G(x, $\mathrm{d}$y, \omega)$. Some examples such as compound Poisson processes, Brownian motion and diffusions are considered.