Perpetual Integral Functionals of Multidimensional Stochastic Processes

Abstract

The paper is devoted to the existence of integral functionals ${\int }_0^{\infty }f(X(t))\mathrm{d}t$ for several classes of processes in $\mathbb{R}$ with $d\ge 3$. Some examples such as Brownian motion, fractional Brownian motion, compound Poisson process, Markov processes admitting densities of transitional probabilities are considered.

11 pages