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November 2018 Representations and isomorphism identities for infinitely divisible processes
Jan Rosiński
Ann. Probab. 46(6): 3229-3274 (November 2018). DOI: 10.1214/17-AOP1246


We propose isomorphism-type identities for nonlinear functionals of general infinitely divisible processes. Such identities can be viewed as an analogy of the Cameron–Martin formula for Poissonian infinitely divisible processes but with random translations. The applicability of such tools relies on precise understanding of Lévy measures of infinitely divisible processes and their representations, which are studied here in full generality. We illustrate this approach on examples of squared Bessel processes, Feller diffusions, permanental processes, as well as Lévy processes.


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Jan Rosiński. "Representations and isomorphism identities for infinitely divisible processes." Ann. Probab. 46 (6) 3229 - 3274, November 2018.


Received: 1 July 2016; Revised: 1 August 2017; Published: November 2018
First available in Project Euclid: 25 September 2018

zbMATH: 06975486
MathSciNet: MR3857855
Digital Object Identifier: 10.1214/17-AOP1246

Primary: 60E07 , 60G15 , 60G17 , 60G51
Secondary: 60G60 , 60G99

Keywords: Dynkin isomorphism theorem , infinitely divisible process , isomorphism identities , Lévy measure on path spaces , series representations , stochastic integral representations

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.46 • No. 6 • November 2018
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