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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 1 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...
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