1,566 research outputs found
Berman's inequality under random scaling
Berman's inequality is the key for establishing asymptotic properties of
maxima of Gaussian random sequences and supremum of Gaussian random fields.
This contribution shows that, asymptotically an extended version of Berman's
inequality can be established for randomly scaled Gaussian random vectors. Two
applications presented in this paper demonstrate the use of Berman's inequality
under random scaling
Dynamic Scaling of Width Distribution in Edwards--Wilkinson Type Models of Interface Dynamics
Edwards--Wilkinson type models are studied in 1+1 dimensions and the
time-dependent distribution, P_L(w^2,t), of the square of the width of an
interface, w^2, is calculated for systems of size L. We find that, using a flat
interface as an initial condition, P_L(w^2,t) can be calculated exactly and it
obeys scaling in the form _\infty P_L(w^2,t) = Phi(w^2 / _\infty,
t/L^2) where _\infty is the stationary value of w^2. For more complicated
initial states, scaling is observed only in the large- time limit and the
scaling function depends on the initial amplitude of the longest wavelength
mode. The short-time limit is also interesting since P_L(w^2,t) is found to
closely approximate the log-normal distribution. These results are confirmed by
Monte Carlo simulations on a `roof-top' model of surface evolution.Comment: 5 pages, latex, 3 ps figures in a separate files, submitted to
Phys.Rev.
A prospective study of the k-factor Gegenbauer processes with heteroscedastic errors and an application to inflation rates
We investigate some statistical properties of the new k-factor Gegenbauer process with heteroscedastic noises One of the goals of the paper is to give tools which permit to use this model to explain the behaviour of certain data sets in finance and in macroeconomics. Monte Carlo experiments are provided to calibrate the theoretical properties. Applications on consumer price indexes and inflation rates are done;GIGARCH process â estimation theory â Inflation rates â prices indexes.
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