Drichlet forms for Poisson measures and Lévy processes : the lent particle method

Nicolas Bouleau; Laurent Denis

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arXiv · 1301.6390

Drichlet forms for Poisson measures and Lévy processes : the lent particle method

Nicolas Bouleau·Laurent Denis

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Abstract

We present a new approach to absolute continuity of laws of Poisson functionals. The theoretical framework is that of local Dirichlet forms as a tool to study probability spaces. The method gives rise to a new explicit calculus that we show first on some simple examples : it consists in adding a particle and taking it back after computing the gradient. Then we apply it to SDE's driven by Poisson measure.

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Nicolas Bouleau, Laurent Denis. 2013-01-27. Drichlet forms for Poisson measures and Lévy processes : the lent particle method. https://arxiv.org/abs/1301.6390

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