31 research outputs found
Extrapolation of Stationary Random Fields
We introduce basic statistical methods for the extrapolation of stationary
random fields. For square integrable fields, we set out basics of the kriging
extrapolation techniques. For (non--Gaussian) stable fields, which are known to
be heavy tailed, we describe further extrapolation methods and discuss their
properties. Two of them can be seen as direct generalizations of kriging.Comment: 52 pages, 25 figures. This is a review article, though Section 4 of
the article contains new results on the weak consistency of the extrapolation
methods as well as new extrapolation methods for -stable fields with
$0<\alpha\leq 1
Central limit theorems for the excursion set volumes of weakly dependent random fields
The multivariate central limit theorems (CLT) for the volumes of excursion
sets of stationary quasi-associated random fields on are proved.
Special attention is paid to Gaussian and shot noise fields. Formulae for the
covariance matrix of the limiting distribution are provided. A statistical
version of the CLT is considered as well. Some numerical results are also
discussed.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ339 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Approximations of the Wiener sausage and its curvature measures
A parallel neighborhood of a path of a Brownian motion is sometimes called
the Wiener sausage. We consider almost sure approximations of this random set
by a sequence of random polyconvex sets and show that the convergence of the
corresponding mean curvature measures holds under certain conditions in two and
three dimensions. Based on these convergence results, the mean curvature
measures of the Wiener sausage are calculated numerically by Monte Carlo
simulations in two dimensions. The corresponding approximation formulae are
given.Comment: Published in at http://dx.doi.org/10.1214/09-AAP596 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org