Perpetual Integral Functionals of Multidimensional Stochastic Processes

The paper is devoted to the existence of integral functionals $\int_0^\infty f(X(t)),{$\mathrm{d}$t}$forseveralclassesofprocessesin$$\mathbb{R}$$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.