Perpetual Integral Functionals of Multidimensional Stochastic Processes

TL;DR

This paper investigates the conditions under which certain integral functionals of multidimensional stochastic processes in  or higher dimensions exist, covering processes like Brownian motion, fractional Brownian motion, and Poisson processes.

Contribution

It provides new criteria for the existence of integral functionals for various classes of multidimensional stochastic processes.

Findings

Established existence conditions for integral functionals in  dimensions

Analyzed processes including Brownian motion, fractional Brownian motion, and Poisson processes

Extended previous results to broader classes of Markov 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.