Une application de la théorie des excursions à une diffusion réfléchie dégénérée. (An application of the theory of excursions to a degenerated reflected diffusion)
type: Item
instance of: scholarly article
title: Une application de la théorie des excursions à une diffusion réfléchie dégénérée. (An application of the theory of excursions to a degenerated reflected diffusion)
zbMATH Open document ID: 0694.60052
DOI: 10.1007/BF01198429
author: Bernard Lapeyre
publication date: 1990-01-01T00:00:00Z
review text: We consider the \(R^ 2\)-valued reflected stochastic differential equation associated with the degenerated differential operator \[ (1/2)\partial^ 2/\partial x^ 2+x \partial /\partial y. \] We study the excursion phenomenon around the point (0,0). We are able to identify the law of the inverse of the local time as a stable subordinator with order 1/4 and to give for it an occupation time formula. These facts enable us to study the behavior of the law of the process near the point (0,0) and to refine, in our case, results obtained by P. Krée (1985) by means of analytical methods.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 4137122
zbMATH Keywords: reflexion
zbMATH Keywords: Skorokhod problem
zbMATH Keywords: local time
zbMATH Keywords: stochastic differential equation
zbMATH Keywords: excursion phenomenon
zbMATH Keywords: occupation time formula
MaRDI profile type: Publication
cites work: Q4077321
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4137122