339 research outputs found
Ergodicity and mixing bounds for the Fisher-Snedecor diffusion
We consider the Fisher-Snedecor diffusion; that is, the Kolmogorov-Pearson
diffusion with the Fisher-Snedecor invariant distribution. In the nonstationary
setting, we give explicit quantitative rates for the convergence rate of
respective finite-dimensional distributions to that of the stationary
Fisher-Snedecor diffusion, and for the -mixing coefficient of this
diffusion. As an application, we prove the law of large numbers and the central
limit theorem for additive functionals of the Fisher-Snedecor diffusion and
construct -consistent and asymptotically normal estimators for the
parameters of this diffusion given its nonstationary observation.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ453 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Rosenblatt distribution subordinated to gaussian random fields with long-range dependence
The Karhunen-Lo\`eve expansion and the Fredholm determinant formula are used
to derive an asymptotic Rosenblatt-type distribution of a sequence of integrals
of quadratic functions of Gaussian stationary random fields on R^d displaying
long-range dependence. This distribution reduces to the usual Rosenblatt
distribution when d=1. Several properties of this new distribution are
obtained. Specifically, its series representation in terms of independent
chi-squared random variables is given, the asymptotic behavior of the
eigenvalues, its L\`evy-Khintchine representation, as well as its membership to
the Thorin subclass of self-decomposable distributions. The existence and
boundedness of its probability density is then a direct consequence.Comment: This paper has 40 pages and it has already been submitte
Intermittency of trawl processes
We study the limiting behavior of continuous time trawl processes which are
defined using an infinitely divisible random measure of a time dependent set.
In this way one is able to define separately the marginal distribution and the
dependence structure. One can have long-range dependence or short-range
dependence by choosing the time set accordingly. We introduce the scaling
function of the integrated process and show that its behavior displays
intermittency, a phenomenon associated with an unusual behavior of moments
On a class of minimum contrast estimators for Gegenbauer random fields
The article introduces spatial long-range dependent models based on the
fractional difference operators associated with the Gegenbauer polynomials. The
results on consistency and asymptotic normality of a class of minimum contrast
estimators of long-range dependence parameters of the models are obtained. A
methodology to verify assumptions for consistency and asymptotic normality of
minimum contrast estimators is developed. Numerical results are presented to
confirm the theoretical findings.Comment: 23 pages, 8 figure
Intermittency and infinite variance: the case of integrated supOU processes
SupOU processes are superpositions of Ornstein-Uhlenbeck type processes with
a random intensity parameter. They are stationary processes whose marginal
distribution and dependence structure can be specified independently.
Integrated supOU processes have then stationary increments and satisfy central
and non-central limit theorems. Their moments, however, can display an unusual
behavior known as "intermittency". We show here that intermittency can also
appear when the processes have a heavy tailed marginal distribution and, in
particular, an infinite variance
Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes
Superpositions of Ornstein-Uhlenbeck type (supOU) processes provide a rich
class of stationary stochastic processes for which the marginal distribution
and the dependence structure may be modeled independently. We show that they
can also display intermittency, a phenomenon affecting the rate of growth of
moments. To do so, we investigate the limiting behavior of integrated supOU
processes with finite variance. After suitable normalization four different
limiting processes may arise depending on the decay of the correlation function
and on the characteristic triplet of the marginal distribution. To show that
supOU processes may exhibit intermittency, we establish the rate of growth of
moments for each of the four limiting scenarios. The rate change indicates that
there is intermittency, which is expressed here as a change-point in the
asymptotic behavior of the absolute moments.Comment: Stochastic Processes and their Application
- …