Wick product and stochastic partial differential equations with Poisson measure
A. Dermoune (1997)
Annales mathématiques Blaise Pascal
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Displaying similar documents to “Poisson stochastic integration in Hilbert spaces”
Wick product and stochastic partial differential equations with Poisson measure
On Poisson and composed Poisson stochastic set functions
A. Prékopa (1957)
Studia Mathematica
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Anticipative calculus with respect to filtered Poisson processes
L. Decreusefond, N. Savy (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Distribution-valued iterated gradient and chaotic decompositions of Poisson jump times functionals.
Nicolas Privault (2002)
Publicacions Matemàtiques
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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.
Some theoretical results about the distribution of a doubly stochastic Poisson process.
Francisco Jiménez Gómez, Mariano J. Valderrama Bonnet (1992)
Extracta Mathematicae
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Splitting the conservation process into creation and annihilation parts
Nicolas Privault (1998)
Banach Center Publications
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The aim of this paper is the study of a non-commutative decomposition of the conservation process in quantum stochastic calculus. The probabilistic interpretation of this decomposition uses time changes, in contrast to the spatial shifts used in the interpretation of the creation and annihilation operators on Fock space.
Quantum stochastic calculus on full Fock space
Michael Skeide (1998)
Banach Center Publications
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We present a new version of integration of time-adapted processes with respect to creation, annihilation and conservation processes on the full Fock space. Among the new features, in the first place, there is a new formulation of adaptedness which is both simpler and more general than the known ones. The new adaptedness allows for processes which are not restricted to be elements of some norm closure of the ∗-algebra which is generated by the basic creation processes.