121 research outputs found
An optimal series expansion of the multiparameter fractional Brownian motion
We derive a series expansion for the multiparameter fractional Brownian
motion. The derived expansion is proven to be rate optimal.Comment: 21 pages, no figures, final version, to appear in Journal of
Theoretical Probabilit
Estimation in a growth study with irregular measurement times
Between 1982 and 1988 a growth study was carried out at the Division of Pediatric Oncology of the University Hospital of Groningen. A special feature of the project was that sample sizes are small and that ages at entry may be very different. In addition the intended design was not fully complied with. This paper highlights some aspects of the statistical analysis which is based on (1) reference scores, (2) statistical procedures allowing for an irregular pattern of measurement times caused by missing data and shifted measurement times
On optimality of regular projective estimators for semimartingale models III:one step improvements
Representations of isotropic Gaussian random fields with homogeneous increments
We present series expansions and moving average representations of isotropic Gaussian random fields with homogeneous increments, making use of concepts of the theory of vibrating strings. We illustrate our results using the example of Lévy’s fractional Brownian motion on R N. Copyright © 2006 Kacha Dzhaparidze et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1
Functional Limit Theorems for Multiparameter Fractional Brownian Motion
We prove a general functional limit theorem for multiparameter fractional
Brownian motion. The functional law of the iterated logarithm, functional
L\'{e}vy's modulus of continuity and many other results are its particular
cases. Applications to approximation theory are discussed.Comment: AMS-LaTeX, 23 page
A Strong-Coupling Approach to the Magnetization Process of Polymerized Quantum Spin Chains
Polymerized quantum spin chains (i.e. spin chains with a periodic modulation
of the coupling constants) exhibit plateaux in their magnetization curves when
subjected to homogeneous external magnetic fields. We argue that the
strong-coupling limit yields a simple but general explanation for the
appearance of plateaux as well as of the associated quantization condition on
the magnetization. We then proceed to explicitly compute series for the plateau
boundaries of trimerized and quadrumerized spin-1/2 chains. The picture is
completed by a discussion how the universality classes associated to the
transitions at the boundaries of magnetization plateaux arise in many cases
from a first order strong-coupling effective Hamiltonian.Comment: 5 pages REVTeX, three PostScript figures included using psfig.st
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