Classes of infinitely divisible distributions on R^d related to the class of selfdecomposable distributions

2009/09/08 by Makoto Maejima, Maejima, Makoto, Muneya Matsui +3
Decision Sciences · Economics, Econometrics and Finance · #60E07 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0909.1409

openalex publication_date 2009/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies new classes of infinitely divisible distributions on R^d. Firstly, the connecting classes with a continuous parameter between the Jurek class and the class of selfdecomposable distributions are revisited. Secondly, the range of the parameter is extended to construct new classes and characterizations in terms of stochastic integrals with respect to Levy processes are given. Finally, the nested subclasses of those classes are discussed and characterized in two ways: One is by stochastic integral representations and another is in terms of Levy measures.

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