 Bifractional Brownian motion for H>1 and 2HK≤1Anna Talarczyk Statistics & Probability Letters, 2020, vol. 157, issue C Abstract: Bifractional Brownian motion on R+ is a two parameter centered Gaussian process with covariance function: RH,K(t,s)=12Kt2H+s2HK−|t−s|2HK,s,t≥0.This process has been originally introduced by Houdré and Villa in Houdré and Villa (2002) in for the range of parameters H∈(0,1] and K∈(0,1]. Since then, the range of parameters, for which RH,K is known to be nonnegative definite has been somewhat extended, but the full range is still not known. We give an elementary proof that RH,K is nonnegative definite for parameters H,K satisfying H>1 and 0<2HK≤1. We show that RH,K can be decomposed into a sum of two nonnegative definite functions. As a side product we obtain a decomposition of the fractional Brownian motion with Hurst parameter H<12 into a sum of time rescaled Brownian motion and another independent self-similar Gaussian process. We also discuss some simple properties of bifractional Brownian motion with H>1. Keywords: Bifractional Brownian motion; Fractional Brownian motion; Positive definite functions; Gaussian processes; Self-similar processes (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:157:y:2020:i:c:s0167715219302743 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2019.108628 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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