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 Electronic Communications in Probability > Vol. 12 (2007) > Paper 17 open journal systems 

Some Extensions of Fractional Brownian Motion and Sub-Fractional Brownian Motion Related to Particle Systems

Tomasz Bojdecki, Institute of Mathematics, University of Warsaw
Luis G Gorostiza, Centro de Investigacion y de Estudios Avanzados, Mexico
Anna Talarczyk, Institute of Mathematics, University of Warsaw

In this paper we study three self-similar, long-range dependence, Gaussian processes. The first one, with covariance
0min(s,t) ua [(t-u)b+(s-u)b]du,
parameters a > -1, -1 < b ≤ 1, |b| ≤ 1 + a, corresponds to fractional Brownian motion for a = 0, -1 < b < 1. The second one, with covariance
(2-h)(sh + th - (1/2)[(s+t)h + |s-t|h]),
parameter 0 < h ≤ 4, corresponds to sub-fractional Brownian motion for 0 < h < 2. The third one, with covariance
-(s2log s + t2log t -(1/2)[(s+t)2 log (s+t) +(s-t)2 log |s-t|]),
is related to the second one. These processes come from occupation time fluctuations of certain particle systems for some values of the parameters.

Full text: PDF | PostScript

Pages: 161-172

Published on: May 16, 2007

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Electronic Communications in Probability. ISSN: 1083-589X