Analysis on the Poisson Space

  • Nicolas PrivaultEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 1982)


In this chapter we give the definition of the Poisson measure on a space of configurations of a metric space X, and we construct an isomorphism between the Poisson measure on X and the Poisson process on R+. From this we obtain the probabilistic interpretation of the gradient D as a finite difference operator and the relation between Poisson multiple stochastic integrals and Charlier polynomials. Using the gradient and divergence operators we also derive an integration by parts characterization of Poisson measures, and other results such as deviation and concentration inequalities on the Poisson space.


Poisson Process Probabilistic Interpretation Stochastic Integral Poisson Random Measure Poisson Measure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of MathematicsCity University of Hong KongHong Kong P.R. China

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