Approximation des trajectoires et temps local des diffusions. (Approximation of trajectories and local times of diffusions)
type: Item
instance of: scholarly article
title: Approximation des trajectoires et temps local des diffusions. (Approximation of trajectories and local times of diffusions)
zbMATH Open document ID: 0674.60032
author: Jean-Marc Azaïs
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77346
review text: For a diffusion process X and its regularizations either by convolution with an approximate identity or by polygonal interpolation, this paper studies convergence of the normalized upcrossing processes of the regularizations to the local time process of the diffusion. The principal part of the paper is concerned with studying the joint density of \(X_{\epsilon}(t)\), \(X^ 1_{\epsilon}(t)\), where \(X_{\epsilon}\) is the regularization obtained by convolution and X is expressible as a function of Brownian motion. A clever conditioning argument is used to address this joint density. Bounds on the behaviour of the joint density are used to provide answers to the question about upcrossings and local time.
reviewed by: Wilfrid S. Kendall
Mathematics Subject Classification ID: 60F25
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 4104096
zbMATH Keywords: convergence in probability
zbMATH Keywords: convergence in \(L^ p\)
zbMATH Keywords: Rice formula
zbMATH Keywords: diffusion
zbMATH Keywords: local time
zbMATH Keywords: upcrossings
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4104096