Representations and isomorphism identities for infinitely divisible processes
| Autor: | Jan Rosiński |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Pure mathematics 60E07 60G15 60G17 60G51 60G60 60G99 Infinitely divisible process Analogy 01 natural sciences Lévy process 010104 statistics & probability symbols.namesake Mathematics::Probability 60E07 isomorphism identities FOS: Mathematics 0101 mathematics Mathematics 60G60 Generality 010102 general mathematics Dynkin isomorphism theorem Probability (math.PR) Lévy measure on path spaces Nonlinear system stochastic integral representations 60G17 60G15 symbols Isomorphism 60G99 Statistics Probability and Uncertainty Bessel function series representations 60G51 Mathematics - Probability |
| Zdroj: | Ann. Probab. 46, no. 6 (2018), 3229-3274 |
| Popis: | 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 these tools relies on a precise understanding of L\'evy measures of infinitely divisible processes and their representations, which are developed here in full generality. We illustrate this approach on examples of squared Bessel processes, Feller diffusions, permanental processes, as well as L\'evy processes. Comment: 43 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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