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Weak Convergence (weak + convergence)

Distribution by Scientific Domains
Mathematics and Statistics75%

Selected Abstracts

The Limiting Density of Unit Root Test Statistics: A Unifying Technique

JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2000
Mithat Gonen
In this note we introduce a simple principle to derive a constructive expression for the density of the limiting distribution, under the null hypothesis, of unit root statistics for an AR(1)-process in a variety of situations. We consider the case of unknown mean and reconsider the well-known situation where the mean is zero. For long-range dependent errors we indicate how the principle might apply again. We also show that in principle the method also works for a near unit root case. Weak convergence and subsequent Karhunen-Loeve expansion of the weak limit of the partial sum process of the errors plays an important role, along with the evaluation of a certain normal type integral with complex mean and variance. For independent and long range dependent errors this weak limit is ordinary and fractional Brownian motion respectively. AMS 1991 subject classification. Primary 62M10; secondary 62E20. [source]

Modelling Long-memory Time Series with Finite or Infinite Variance: a General Approach

JOURNAL OF TIME SERIES ANALYSIS, Issue 1 2000
Remigijus Leipus
We present a class of generalized fractional filters which is stable with respect to series and parallel connection. This class extends the so-called fractional ARUMA and fractional ARMA filters previously introduced by e.g. Goncalves (1987) and Robinson (1994) and recently studied by Giraitis and Leipus (1995) and Viano et al. (1995). Conditions for the existence of the induced stationary S,S and L2 processes are given. We describe the asymptotic dependence structure of these processes via the codifference and the covariance sequences respectively. In the L2 case, we prove the weak convergence of the normalized partial sums. [source]

Variable cirrus shading during CSIP IOP 5.

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 628 2007
I: Effects on the initiation of convection
Abstract Observations from the Convective Storm Initiation Project (CSIP) show that on 29 June 2005 (Intensive Observation Period 5) cirrus patches left over from previous thunderstorms reduced surface sensible and latent heat fluxes in the CSIP area. Large-eddy model (LEM) simulations, using moving positive surface-flux anomalies, show that we expect the observed moving gaps in the cirrus cover to significantly aid convective initiation. In these simulations, the timing of the CI is largely determined by the amount of heat added to the boundary layer, but weak convergence at the rear edge of the moving anomalies is also significant. Meteosat and rain-radar data are combined to determine the position of convective initiation for all 25 trackable showers in the CSIP area. The results are consistent with the LEM simulations, with showers initiating at the rear edge of gaps, at the leading edge of the anvil, or in clear skies, in all but one of the cases. The initiation occurs in relatively clear skies in all but two of the cases, with the exceptions probably linked to orographic effects. For numerical weather prediction, the case highlights the importance of predicting and assimilating cloud cover. The results show that in the absence of stronger forcings, weak forcings, such as from the observed cirrus shading, can determine the precise location and timing of convective initiation. In such cases, since the effects of shading by cirrus anvils from previous convective storms are relatively unpredictable, this is expected to limit the predictability of the convective initiation. Copyright © 2007 Royal Meteorological Society [source]

Approach to self-similarity in Smoluchowski's coagulation equations

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 9 2004
Govind Menon
We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's equations of coagulation for the solvable kernels K(x, y) = 2, x + y and xy. In addition to the known self-similar solutions with exponential tails, there are one-parameter families of solutions with algebraic decay, whose form is related to heavy-tailed distributions well-known in probability theory. For K = 2 the size distribution is Mittag-Leffler, and for K = x + y and K = xy it is a power-law rescaling of a maximally skewed ,-stable Lévy distribution. We characterize completely the domains of attraction of all self-similar solutions under weak convergence of measures. Our results are analogous to the classical characterization of stable distributions in probability theory. The proofs are simple, relying on the Laplace transform and a fundamental rigidity lemma for scaling limits. © 2003 Wiley Periodicals, Inc. [source]