Poisson stochastic integration in Hilbert spaces
Nicolas Privault, Jiang-Lun Wu (1999)
Annales mathématiques Blaise Pascal
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Nicolas Privault, Jiang-Lun Wu (1999)
Annales mathématiques Blaise Pascal
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Jean Bertoin, Jean-François Le Gall (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Francisco Jiménez Gómez, Mariano J. Valderrama Bonnet (1992)
Extracta Mathematicae
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Nicolas Privault, Jean-Claude Zambrini (2004)
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L. Decreusefond, N. Savy (2006)
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K. Urbanik (1997)
Colloquium Mathematicum
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The paper deals with nonnegative stochastic processes X(t,ω)(t ≤ 0) not identically zero with stationary and independent increments right-continuous sample functions and fulfilling the initial condition X(0,ω)=0. The main aim is to study the moments of the random functionals for a wide class of functions f. In particular a characterization of deterministic processes in terms of the exponential moments of these functionals is established.