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Metric unconditionality and Fourier analysis

Stefan Neuwirth (1998)

Studia Mathematica

We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces L E p ( ) and C E ( ) of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces p E ( ) , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between L E p ( ) and L E p + 2 ( ) . These...

Metrics for multivariate stable distributions

John P. Nolan (2010)

Banach Center Publications

Metrics are proposed for the distance between two multivariate stable distributions. The first set of metrics are defined in terms of the closeness of the parameter functions of one dimensional projections of the laws. Convergence in these metrics is equivalent to convergence in distribution and an explicit bound on the uniform closeness of two stable densities is given. Another metric based on the Prokhorov metric between the spectral measures is related to the first metric. Consequences for approximation,...

Micro tangent sets of continuous functions

Zoltán Buczolich (2003)

Mathematica Bohemica

Motivated by the concept of tangent measures and by H. Fürstenberg’s definition of microsets of a compact set A we introduce micro tangent sets and central micro tangent sets of continuous functions. It turns out that the typical continuous function has a rich (universal) micro tangent set structure at many points. The Brownian motion, on the other hand, with probability one does not have graph like, or central graph like micro tangent sets at all. Finally we show that at almost all points Takagi’s...

Microscopic concavity and fluctuation bounds in a class of deposition processes

Márton Balázs, Júlia Komjáthy, Timo Seppäläinen (2012)

Annales de l'I.H.P. Probabilités et statistiques

We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have order of magnitude t1/3. This is in agreement with the expectation that these systems lie in the same KPZ universality class as the asymmetric simple exclusion process. The result is via a robust argument formulated for a broad class of deposition-type processes....

Milstein’s type schemes for fractional SDEs

Mihai Gradinaru, Ivan Nourdin (2009)

Annales de l'I.H.P. Probabilités et statistiques

Weighted power variations of fractional brownian motion B are used to compute the exact rate of convergence of some approximating schemes associated to one-dimensional stochastic differential equations (SDEs) driven by B. The limit of the error between the exact solution and the considered scheme is computed explicitly.

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