Distribution-valued iterated gradient and chaotic decompositions of Poisson jump times functionals
TL;DR: In this article, a class of distributions on Poisson space which allows to iterate a modification of the gradient of the Poisson process is defined, and a formula for the chaos expansion of functionals of jump times of Poisson processes is given.
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Abstract: We define a class of distributions on Poisson space which allows to iterate a modification of the gradient of [1]. As an application we obtain, with relatively short calculations, a formula for the chaos expansion of functionals of jump times of the Poisson process
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References
Anticipative calculus for the Poisson process based on the Fock space
David Nualart,Josep Vives +1 more
- 01 Jan 1990
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.org/conditions) of the agreement with the séminaire de probabilités (Strasbourg) are discussed.
Connection, parallel transport, curvature and energy identities on spaces of configurations
TL;DR: In this article, a construction repose sur l'introduction d'un fibre tangent particulier and de son gradient amorti associe, ainsi que sur la compensation de quantites divergentes.
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Multiple stochastic integral expansions of arbitrary Poisson jump times functionals
TL;DR: In this paper, the Wiener-Poisson expansion of square-integrable functionals of a finite number of Poisson jump times in series of multiple Poisson stochastic integrals is studied.
6
Integration by parts for Poisson processes
TL;DR: Using a perturbation of the rate of a Poisson process and an inverse time change, an integration by parts formula is obtained in this paper, which enables a new form of the integrand in a martingale representation result to be obtained.
Differential Calculus and Integration by Parts on Poisson Space
Eric A. Carlen,Etienne Pardoux +1 more
- 01 Jan 1990
TL;DR: In this article, a gradient operator on random variables defined on the standard Poisson space is defined, and an integration by parts (integration by parts) formula shows that the adjoint of that operator extends the usual stochastic integral.