PUB - Publikationen an der Universität Bielefeld

The paper is devoted to the existence of perpetual integral functionals integral(infinity)(0)f(X(t)) dt for several classes of d-dimensional of stochastic processes X (t). The method is very simple: we establish the conditions supplying that these functionals have a finite expectation. Examples of these classes include d-dimensional fractional Brownian motion having coordinates with the same Hurst index H, for which existence is established under the assumption d > 1/H. in In particular, perpetual integral functionals exist for d-dimensional Brownian motion with d > 2, compound Poisson process, Markov processes admitting densities of transitional probabilities. In the case of Brownian motion and fractional Brownian motion we establish that the perpetual integral functionals are not a constant a.s. if f not equal 0.