Convergence in fractional models and applications
type: Item
instance of: scholarly article
title: Convergence in fractional models and applications
zbMATH Open document ID: 1070.60022
author: Corinne Berzin
author: José R. León
published in: Electronic Journal of Probability
publication date: 2005-03-08T00:00:00Z
full work available at URL: https://eudml.org/doc/125065
full work available at URL: paper10.abs.html
review text: Let \(b_{\alpha}\) be fractional Brownian motion with Hurst parameter \(\alpha\in (0,1)\) and let \(X\) be the solution of the stochastic differential equation \(dX(t)=\sigma(X(t))\,db_{\alpha}(t)\) on \([0,\infty)\) with \(X(0)=c\). To regularize the processes consider a positive kernel with \(L^1\)-norm equal to one, define \(\varphi_{\varepsilon}(t)=\varphi(t/\varepsilon)/\varepsilon\) and set \(b_{\alpha}^{\varepsilon}=\varphi_{\varepsilon}\ast b_{\alpha}\) and \(X^{\varepsilon}=\varphi_{\varepsilon}\ast X\), respectively. The authors discuss for the process \(b_{\alpha}^{\varepsilon}\) and functionals of this process like \(X^{\varepsilon}\) the relation of level crossings to local time and the rate of convergence of the involved limit theorem. Moreover, they analyze the rate of convergence of a limit theorem concerning the increments of fractional Brownian motion. Finally, the authors propose probabilistic and statistical applications of their results.
reviewed by: Andreas Martin
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G18
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 62F03
zbMATH DE Number: 2142164
zbMATH Keywords: Level crossings
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: limit theorem
zbMATH Keywords: local time
zbMATH Keywords: rate of convergence
MaRDI profile type: Publication
DOI: 10.1214/EJP.V10-172
description: scientific article; zbMATH DE number 2142164