Particle picture interpretation of some Gaussian processes related to fractional Brownian motion

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• 作者：Tomasz Bojdecki ^{tobojd@mimuw.edu.pl} ; Anna Talarczyk ; ^{annatal@mimuw.edu.pl}
• 关键词：Primary ; 60G15 ; 60F05 ; Secondary ; 60G20 ; 60G52 ; 60J80
• 刊名：Stochastic Processes and their Applications
• 出版年：2012
• 期刊代码：57_03044149
• 类别：mt
• 出版时间：May, 2012
• 卷：122
• 期：5
• 页码：2134-2154
• 文件大小：274 K

摘要

We construct fractional Brownian motion, sub-fractional Brownian motion and negative sub-fractional Brownian motion by means of limiting procedures applied to some particle systems. These processes are obtained for full ranges of Hurst parameter.

We employ the so-called white noise approach. Our construction is quite general, permitting to obtain also some other Gaussian processes, as well as multidimensional random fields. In particular, we generalize and presumably simplify some results by Hambly and Jones (2007). We also obtain a new class of -valued density processes, containing as a particular case the density process of Martin-L枚f (1976).