Representations and isomorphism identities for infinitely divisible\n processes

2016/07/26 by J. Rosiński, Rosinski, Jan
Economics, Econometrics and Finance · #60E07 #60G15 #60G17 #60G51 #60G60 #60G99 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1607.07862

openalex publication_date 2016/07/26 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We propose isomorphism type identities for nonlinear functionals of general\ninfinitely divisible processes. Such identities can be viewed as an analogy of\nthe Cameron-Martin formula for Poissonian infinitely divisible processes but\nwith random translations. The applicability of these tools relies on a precise\nunderstanding of L 'evy measures of infinitely divisible processes and their\nrepresentations, which are developed here in full generality. We illustrate\nthis approach on examples of squared Bessel processes, Feller diffusions,\npermanental processes, as well as L 'evy processes.\n

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