We give a representation of the Gamma subordinator as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms. In particular, we have obtained Krein representations of the subordinators which govern the two parameter Poisson–Dirichlet family of distributions .
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Catherine Donati-Martin, Marc Yor, Some Explicit Krein Representations of Certain Subordinators, Including the Gamma Process. Publ. Res. Inst. Math. Sci. 42 (2006), no. 4, pp. 879–895