37,608 research outputs found
Inference for the limiting cluster size distribution of extreme values
Any limiting point process for the time normalized exceedances of high levels
by a stationary sequence is necessarily compound Poisson under appropriate long
range dependence conditions. Typically exceedances appear in clusters. The
underlying Poisson points represent the cluster positions and the
multiplicities correspond to the cluster sizes. In the present paper we
introduce estimators of the limiting cluster size probabilities, which are
constructed through a recursive algorithm. We derive estimators of the extremal
index which plays a key role in determining the intensity of cluster positions.
We study the asymptotic properties of the estimators and investigate their
finite sample behavior on simulated data.Comment: Published in at http://dx.doi.org/10.1214/07-AOS551 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Geometric ergodicity for some space-time max-stable Markov chains
Max-stable processes are central models for spatial extremes. In this paper,
we focus on some space-time max-stable models introduced in Embrechts et al.
(2016). The processes considered induce discrete-time Markov chains taking
values in the space of continuous functions from the unit sphere of
to . We show that these Markov chains are
geometrically ergodic. An interesting feature lies in the fact that the state
space is not locally compact, making the classical methodology inapplicable.
Instead, we use the fact that the state space is Polish and apply results
presented in Hairer (2010)
Tails of random sums of a heavy-tailed number of light-tailed terms
The tail of the distribution of a sum of a random number of independent and
identically distributed nonnegative random variables depends on the tails of
the number of terms and of the terms themselves. This situation is of interest
in the collective risk model, where the total claim size in a portfolio is the
sum of a random number of claims. If the tail of the claim number is heavier
than the tail of the claim sizes, then under certain conditions the tail of the
total claim size does not change asymptotically if the individual claim sizes
are replaced by their expectations. The conditions allow the claim number
distribution to be of consistent variation or to be in the domain of attraction
of a Gumbel distribution with a mean excess function that grows to infinity
sufficiently fast. Moreover, the claim number is not necessarily required to be
independent of the claim sizes.Comment: Accepted for publication in Insurance: Mathematics and Economic
Cladding for transverse-pumped solid-state laser
In a transverse pumped, solid state laser, a nonabsorptive cladding surrounds a gain medium. A single tranverse mode, namely the Transverse Electromagnetic (TEM) sub 00 mode, is provided. The TEM sub 00 model has a cross sectional diameter greater than a transverse dimension of the gain medium but less than a transverse dimension of the cladding. The required size of the gain medium is minimized while a threshold for laser output is lowered
Dual band fss with fractal elements
Experimental and computed results of a frequency selective surface (FSS) based on a certain type of fractal element are presented. The fractal element is a two iteration Sierpinski gasket dipole. Owing to the dual band behaviour of the two iteration Sierpinski gasket dipole, two stopbands are exhibited within the operating frequency band. This behaviour is obtained by arraying one simple element in a single layer frequency selective surface (FSS)Peer ReviewedPostprint (published version
Hydromechanics of low-Reynolds-number flow. Part 5. Motion of a slender torus
In order to elucidate the general Stokes flow characteristics present for slender bodies of finite centre-line curvature the singularity method for Stokes flow has been employed to construct solutions to the flow past a slender torus. The symmetry of the geometry and absence of ends has made a highly accurate analysis possible. The no-slip boundary condition on the body surface is satisfied up to an error term of O(E^2 ln E), where E is the slenderness parameter (ratio of cross-sectional radius to centre-line radius). This degree of accuracy makes it possible to determine the force per unit length experienced by the torus up to a term of O(E^2). A comparison is made between the force coefficients of the slender torus to those of a straight slender body to illustrate the large differences that may occur as a result of the finite centre-line curvature
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