Absolute continuity and convergence in variation for distributions of functionals of Poisson point measure

Details Absolute continuity and convergence in variation for distributions of functionals of Poisson point measure Absolute continuity and convergence in variation for distributions of functionals of Poisson point measure

2008-03-17

arxiv.org/abs/0803.2389v2

Mathematics

Probability

Accepted for publication in Journal of Theoretical Probability; manuscript number #JOTP-248R1

Scientific paper

General sufficient conditions are given for absolute continuity and convergence in variation of the distributions of the unctionals on a probability space, generated by a Poisson point measure. The phase space of the Poisson point measure is supposed to be of the form (0,\infty)\times U, and its intensity measure to be equal dt\Pi(du). We introduce the family of time stretching transformations of the configurations of the point measure. The sufficient conditions for absolute continuity and convergence in variation are given in the terms of the time stretching transformations and the relative differential operators. These conditions are applied to solutions of SDE's driven by Poisson point measures, including an SDE's with non-constant jump rate.

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