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March 2009 Clark–Ocone formula and variational representation for Poisson functionals
Xicheng Zhang
Ann. Probab. 37(2): 506-529 (March 2009). DOI: 10.1214/08-AOP411


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. "Clark–Ocone formula and variational representation for Poisson functionals." Ann. Probab. 37 (2) 506 - 529, March 2009.


Published: March 2009
First available in Project Euclid: 30 April 2009

zbMATH: 1179.60037
MathSciNet: MR2510015
Digital Object Identifier: 10.1214/08-AOP411

Primary: 60F10 , 60H07

Keywords: Clark–Ocone formula , Girsanov theorem , Poisson functional , variational representation

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 2 • March 2009
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