Self-similar processes with independent increments associated with Levy and Bessel processes

摘要

Wolfe (Stochastic Process. Appl. 12(3) (1982) 301) and Sato (Probab. Theory Related Fields 89(3) (1991) 285) gave two different representations of a random variable X, with a self-decomposable distribution in terms of processes with independent increments. This paper shows how either of these representations follows easily from the other, and makes these representations more explicit when X-1 is either a first or last passage time for a Bessel process. (C) 2002 Elsevier Science B.V. All rights reserved. [References: 31]