Clark--Ocone formula and variational representation for Poisson functionals

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.

Published in at http://dx.doi.org/10.1214/08-AOP411 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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