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Étude d'une EDPS conduite par un bruit poissonnien
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  • Published: June 1998

Étude d'une EDPS conduite par un bruit poissonnien

  • Erwan Saint Loubert Bié1 

Probability Theory and Related Fields volume 111, pages 287–321 (1998)Cite this article

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Summary.

We study a Stochastic Partial Differential Equation, of parabolic type, set on ℝd, with d∈ℕ. This equation is driven by a Poisson random measure, either compensated or not. The first part of this work shows existence and uniqueness of a progressively measurable solution. The technics involved are close to those used to deal with analogous equations driven by a Gaussian noise. The second part gives some criterions on the intensity of the Poisson random measure, in order to ensure some smoothness, either in space or in time, for the solution of this equation.

Résumé

. Nous étudions une équation aux dérivées partielles stochastique (EDPS), de type parabolique, posée sur ℝd, d entier, et conduite par un bruit poissonnien, compensé ou non. La première partie de ce travail montre l'existence et l'unicité d'une solution progressivement mesurable. Les techniques employées sont proches de celles utilisées pour résoudre les équations analogues conduites par un bruit blanc. La seconde partie donne des conditions, portant sur l'intensité du bruit poissonnien, et permettant d'assurer certaines régularités, en espace ou bien en temps, pour le processus solution.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Appliquées, UMR 6620 du CNRS Université Blaise Pascal, F-63177 Aubière Cedex, France. e-mail: sloubert@ucfma.univ-bpclermont.fr, , , , , , FR

    Erwan Saint Loubert Bié

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  1. Erwan Saint Loubert Bié
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Received: 7 April 1997/In revised form: 20 January 1998

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Saint Loubert Bié, E. Étude d'une EDPS conduite par un bruit poissonnien. Probab Theory Relat Fields 111, 287–321 (1998). https://doi.org/10.1007/s004400050169

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  • Issue Date: June 1998

  • DOI: https://doi.org/10.1007/s004400050169

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  • Mathematics Subject Classification (1991): 60H15
  • 35R60
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