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Composition with distributions of Wiener‐Poisson variables and its asymptotic expansion
Author(s) -
Hayashi Masafumi,
Ishikawa Yasushi
Publication year - 2012
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.200910194
Subject(s) - mathematics , malliavin calculus , poisson distribution , jump , jump diffusion , asymptotic expansion , compound poisson process , distribution (mathematics) , integral representation theorem for classical wiener space , type (biology) , mathematical analysis , pure mathematics , poisson process , statistics , integral equation , functional integration , differential equation , ecology , stochastic partial differential equation , physics , quantum mechanics , biology
In this paper, we introduce the compositions of smooth Wiener‐Poisson functional and Schwartz distribution by using Malliavin calculus jump type. We also prove Watanabe's theorem in the jump‐diffusion case, that is, the asymptotic expansion formula for the compositions of a smooth Wiener‐Poisson functional with Schwartz distributions.