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Your search keyword '"Laurent Decreusefond"' showing total 2 results
Start Over Author "Laurent Decreusefond" Journal comptes rendus mathematique
2 results on '"Laurent Decreusefond"'

1. Moment formulae for general point processes

Author

Ian Flint, Laurent Decreusefond, Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), and Télécom ParisTech

Subjects
Measure transformation, Moments, Malliavin calculus, Point processes, Mathematical proof, 01 natural sciences, Stochastic integral, Point process, 010104 statistics & probability, Moment measure, FOS: Mathematics, Applied mathematics, 0101 mathematics, Mathematics, Stochastic process, Probability (math.PR), 010102 general mathematics, Mathematical analysis, Order (ring theory), General Medicine, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Moment (mathematics), Transformation (function), Mathematics - Probability, Analysis
Abstract

The goal of this paper is to generalize most of the moment formulae obtained in [12] . More precisely, we consider a general point process μ, and show that the quantities relevant to our problem are the so-called Papangelou intensities. When the Papangelou intensities of μ are well-defined, we show some general formulae to recover the moment of order n of the stochastic integral of the point process. We will use these extended results to introduce a divergence operator and study a random transformation of the point process.

Published
2014

2. Stochastic integration with respect to Gaussian processes

Author

Laurent Decreusefond

Subjects
Stochastic process, Mathematical analysis, Hilbert space, General Medicine, Absolute continuity, Stochastic integral, Stochastic integration, symbols.namesake, symbols, Applied mathematics, Itō's lemma, Gaussian process, Brownian motion, Mathematics
Abstract

We construct a Stratonovitch–Skorohod-like stochastic integral for general Gaussian processes. We study its sample path regularity and one of its numerical approximating schemes. We also analyze the way it is transformed by an absolutely continuous change of probability and we give an Ito formula. To cite this article: L. Decreusefond, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 903–908.

Published
2002

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