52 research outputs found
Limit theorems for weighted functionals of cyclical long-range dependent random fields
The paper investigates isotropic random fields for which the spectral density
is unbounded at some frequencies. Limit theorems for weighted functionals of
these random fields are established. It is shown that for a wide class of
functionals, which includes the Donsker scheme, the limit is not affected by
singularities at non-zero frequencies. For general schemes, in contrast to the
Donsker line, we demonstrate that the singularities at non-zero frequencies
play a role even for linear functionals.Comment: 19 pages, 2 figures. This is an Author's Accepted Manuscript of an
article in the Stochastic Analysis and Applications, Vol. 31, No. 2. (2013),
199--213. [copyright Taylor \& Francis], available online at:
http://www.tandfonline.com/ [DOI:10.1080/07362994.2013.741410
Sojourn measures of Student and Fisher-Snedecor random fields
Limit theorems for the volumes of excursion sets of weakly and strongly
dependent heavy-tailed random fields are proved. Some generalizations to
sojourn measures above moving levels and for cross-correlated scenarios are
presented. Special attention is paid to Student and Fisher-Snedecor random
fields. Some simulation results are also presented.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ529 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Tauberian and Abelian theorems for long-range dependent random fields
This paper surveys Abelian and Tauberian theorems for long-range dependent
random fields. We describe a framework for asymptotic behaviour of covariance
functions or variances of averaged functionals of random fields at infinity and
spectral densities at zero. The use of the theorems and their limitations are
demonstrated through applications to some new and less-known examples of
covariance functions of long-range dependent random fields.Comment: Will appear in Methodology and Computing in Applied Probability. 26
pages, 10 figures. The final publication is available at link.springer.com.
DOI: 10.1007/s11009-012-9276-
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