Clark--Ocone formula and variational representation for Poisson functionals
Probability
2009-06-10 v1
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.
Cite
@article{arxiv.0906.1721,
title = {Clark--Ocone formula and variational representation for Poisson functionals},
author = {Xicheng Zhang},
journal= {arXiv preprint arXiv:0906.1721},
year = {2009}
}
Comments
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)