Excursion measure away from an exit boundary of one-dimensional diffusion processes
type: Item
instance of: scholarly article
title: Excursion measure away from an exit boundary of one-dimensional diffusion processes
zbMATH Open document ID: 1113.60084
author: Kouji Yano
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2007-02-01T00:00:00Z
review text: A measure generalizing the excursion measure away from an exit boundary is constructed for a one-dimensional diffusion process via the desintegration formula with respect to the lifetime. It is used to generalize the convergence theorem of \textit{Y. Kasahara} and \textit{S. Watanabe} [Ill. J. Math. 50, No. 1--4, 515--539 (2006; Zbl 1102.60066)] in terms of the Poisson point fields, where the inverse local time processes of regular diffusions converge in law to a Lévy process related to a diffusion with an exit boundary.
reviewed by: Heinrich Hering
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60G52
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 5120443
zbMATH Keywords: diffusion process
zbMATH Keywords: excursion theory
zbMATH Keywords: Poisson point process
zbMATH Keywords: limit theorem
zbMATH Keywords: stable process
zbMATH Keywords: Krein's spectral theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1166642162
OpenAlex ID: W1987530561
Wikidata QID: Q58331065
cites work: Q3975586
DOI: 10.2977/PRIMS/1166642162
Recommended article: One-dimensional diffusions and their exit spaces.
Recommended article: Approximation of exit times for one-dimensional linear diffusion processes
Recommended article: Exponential estimates in exit probability for some diffusion processes in hilbert spaces
Recommended article: Q3680008
Recommended article: On the Distribution Density of the First Exit Point of a Diffusion Process form a Small Neighborhood of Its Initial Position
Recommended article: Estimators for exit distributions of diffusion processes
Recommended article: Integral Representations of Certain Measures in the One-Dimensional Diffusions Excursion Theory
Recommended article: On the Exit of a Random Walk From a Curvilinear Boundary
Recommended article: One-dimensional diffusions in bounded domains with a possible jump-like exit from a sticky boundary
description: scientific article; zbMATH DE number 5120443