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Some Uses of Point Processes in Multiple Stochastic Integration
Author(s) -
Kallenberg Olav
Publication year - 1991
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19911510102
Subject(s) - mathematics , point process , poisson distribution , divergence (linguistics) , infinity , decoupling (probability) , poisson point process , series (stratigraphy) , compound poisson process , skewness , poisson process , calculus (dental) , mathematical analysis , statistics , medicine , paleontology , philosophy , linguistics , dentistry , control engineering , engineering , biology
We discuss a number of topics relating to multiple stochastic integration, where notions and ideas from point process theory seem particularly useful. Thus we give conditions for summability of certain multiple random series in terms of associated Poisson integrals, prove a decoupling result for divergence in probability to infinity, and give conditions for the existence of certain multiple integrals with respect to compensated POISSON and asymmetric LÉVY processes. In particular, the existence criteria for multiple p ‐stable integrals are shown to be independent of the skewness parameter.