Remarks on the intersection local time of fractional Brownian motions
type: Item
instance of: scholarly article
title: Remarks on the intersection local time of fractional Brownian motions
zbMATH Open document ID: 1225.60062
author: Litan Yan
author: Chao Chen
published in: Statistics \& Probability Letters
publication date: 2011-07-26T00:00:00Z
review text: The existence of the so-called intersection local time \[ I(B^H,\widetilde B^H)\equiv\int_0^T\int_0^T\delta(B_t^H-\widetilde B_s^H)\,ds\,dt, \] where \(\delta(x)\) is the Dirac delta function was given by \textit{D. Nualart} and \textit{S. Ortiz-Latorre} [J. Theor. Probab. 20, No. 4, 759--767 (2007; Zbl 1154.60028)]. The authors give another proof for the existence of the random variable \(I(B^H,\widetilde B^H)\) in \(L^2\). They also discuss necessary and sufficient conditions for the intersection local time process to be smooth in the sense of Meyer-Watanabe.
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 60G22
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60H07
zbMATH DE Number: 5932052
zbMATH Keywords: intersection local time
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: chaos expansion
MaRDI profile type: Publication
full work available at URL: j.spl.2011.01.021
OpenAlex ID: W2159978736
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DOI: 10.1016/J.SPL.2011.01.021
description: scientific article; zbMATH DE number 5932052