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arXiv · 0906.1721

Clark--Ocone formula and variational representation for Poisson functionals

Xicheng Zhang
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Abstract

In this paper we first prove a Clark--Ocone formula for any bounded measurable functional on Poisson space. Then using this formula, under some conditions on the intensity measure of Poisson random measure, we prove a variational representation formula for the Laplace transform of bounded Poisson functionals, which has been conjectured by Dupuis and Ellis [A Weak Convergence Approach to the Theory of Large Deviations (1997) Wiley], p. 122.

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Xicheng Zhang. 2009-06-09. Clark--Ocone formula and variational representation for Poisson functionals. https://doi.org/10.1214/08-aop411

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