Author(s) :
Jochen Blath
,
Andreas Martin
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 25-2006
MSC 2000
- 60G15 Gaussian processes
-
60G17 Sample path properties
-
60G60 Random fields
Abstract :
Let $X$ be a semi-fractional Brownian sheet, that is
a centred and continuous Gaussian random field with
$\mathbb E [X(s,t)X(\hat{s},\hat{t}\,)] = (t\wedge \hat{t}\,)
(s^\alpha + \hat{s}^\alpha-|s-\hat{s}|^\alpha)/2$.
We provide, for $\alpha\in(0,2)$, an analysis of the propagation of
singularities into the fractional direction of $X$. Here,
singularities are times where the law of the iterated
logarithm fails, such as fast points.
Keywords :
Propagation of singularities, fractional Brownian motion, semi-fractional Brownian sheet, Gaussian random field, fast points