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Stochastic Analysis for Poisson Point Processes
The first four surveys can be seen as a “crash course” in stochastic analysis on
the Poisson space. Starting from the careful construction of Malliavin operators
on abstract Poisson spaces via Fock space representations (G. Last), the elegant
combinatorial properties of (multiple) Poisson stochastic integrals are explored (N.
Privault) and an introduction provided to variational formulae, allowing the reader to
deal with the analytical study of expectations of Poisson functionals (I. Molchanov
and S. Zuyev). Finally, J.-L. Solé and F. Utzet show how these tools can be extended
to the more general framework of random measures with independent increments
(sometimes called completely random measures) and Lévy processes
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