Anticipative calculus with respect to filtered Poisson processes

Laurent Decreusefond; Nicolas Savy

doi:10.1016/j.anihpb.2005.03.005

Anticipative calculus with respect to filtered Poisson processes

Laurent Decreusefond
, Nicolas Savy

CNRS LTCI
UMR 6625

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We construct the basis of a stochastic calculus for a new class of processes: filtered Poisson processes. These processes are defined by an fBm-like stochastic integral but a Poisson process is subsided to the Brownian motion. We use Malliavin calculus to first construct a gradient then a divergence operator, which will play the role of an anticipative stochastic integral. We study into details the sample-paths regularity of this integral and give an Itô formula for Itô-like processes.

langue originale	Anglais
Pages (de - à)	343-372
Nombre de pages	30
journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	42
Numéro de publication	3
Les DOIs	https://doi.org/10.1016/j.anihpb.2005.03.005
état	Publié - 1 janv. 2006

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10.1016/j.anihpb.2005.03.005

Contient cette citation

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title = "Anticipative calculus with respect to filtered Poisson processes",

abstract = "We construct the basis of a stochastic calculus for a new class of processes: filtered Poisson processes. These processes are defined by an fBm-like stochastic integral but a Poisson process is subsided to the Brownian motion. We use Malliavin calculus to first construct a gradient then a divergence operator, which will play the role of an anticipative stochastic integral. We study into details the sample-paths regularity of this integral and give an It{\^o} formula for It{\^o}-like processes.",

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AB - We construct the basis of a stochastic calculus for a new class of processes: filtered Poisson processes. These processes are defined by an fBm-like stochastic integral but a Poisson process is subsided to the Brownian motion. We use Malliavin calculus to first construct a gradient then a divergence operator, which will play the role of an anticipative stochastic integral. We study into details the sample-paths regularity of this integral and give an Itô formula for Itô-like processes.

KW - Anticipative calculus

KW - Malliavin calculus

KW - Poisson process

KW - Shot-noise process

KW - Stochastic integral

U2 - 10.1016/j.anihpb.2005.03.005

DO - 10.1016/j.anihpb.2005.03.005

M3 - Article

AN - SCOPUS:33645320236

SN - 0246-0203

VL - 42

SP - 343

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JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 3

ER -

Anticipative calculus with respect to filtered Poisson processes

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