On bifractional Brownian motion
type: Item
instance of: scholarly article
title: On bifractional Brownian motion
zbMATH Open document ID: 1100.60019
author: Francesco Russo
author: Ciprian A. Tudor
published in: Stochastic Processes and their Applications
publication date: 2006-06-30T00:00:00Z
review text: The bifractional Brownian motion \((B_t^{H,K})\) is defined, for \(0< H<1\) and \(0<K\leq 1\), as the centered Gaussian process started from 0 having covariance: \[ (s,t)\mapsto 2^{-K}[(s^{2H}+t^{2H})^K-|s-t|^{2HK}]. \] It is \(HK\)-self-similar, and Hölder continuous of any order \(<HK\). The authors establish in particular that: -- \(\lim_{\varepsilon \searrow 0}\int^t_0|B_{s+\varepsilon}^{H,K}-B_s^{H,K}|^{1/HK}ds= c_{H,K}\times t\) exists in probability; -- \(B^{H,K}\) is not a semi-martingale, nor a Markov process (of course except if \(2H=K=1)\); -- \((B^{H,K}+W)\) has the law of \(W\), if \(HK>\frac 34\), for any independent Wiener process \(W\); -- \(B^{H,K}\) has short memory if \(2HK\leq 1\); -- \(B^{H,K}\) admits a local time, in the space \(\mathbb{D}^{\alpha,2}\) for \(\alpha<\frac {1}{2HK}-\frac 12\).
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 60G18
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 5037282
zbMATH Keywords: Dirichlet processes
zbMATH Keywords: self-similar processes
zbMATH Keywords: calculus via regularization
MaRDI profile type: Publication
full work available at URL: j.spa.2005.11.013
OpenAlex ID: W2056464302
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DOI: 10.1016/J.SPA.2005.11.013
description: scientific article