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Ind-additive functionals on random vectors

CONTENTS1. Introduction.......................................................................................................................................................................... 52. Preliminaries....................................................................................................................................................................... 63. Random vector measures...................................................................................................................................................

Strong laws of large numbers in certain linear spaces

Wojbor A. Woyczynski — 1974

Annales de l'institut Fourier

In this paper we are concerned with the norm almost sure convergence of series of random vectors taking values in some linear metric spaces and strong laws of large numbers for sequences of such random vectors. Section 2 treats the Banach space case where the results depend upon the geometry of the unit cell. Section 3 deals with spaces equipped with a non-necessarily homogeneous F -norm and in Section 4 we restrict our attention to sequences of identically distributed random vectors.

Asymptotics for conservation laws involving Lévy diffusion generators

Piotr BilerGrzegorz KarchWojbor A. Woyczyński — 2001

Studia Mathematica

Let -ℒ be the generator of a Lévy semigroup on L¹(ℝⁿ) and f: ℝ → ℝⁿ be a nonlinearity. We study the large time asymptotic behavior of solutions of the nonlocal and nonlinear equations uₜ + ℒu + ∇·f(u) = 0, analyzing their L p -decay and two terms of their asymptotics. These equations appear as models of physical phenomena that involve anomalous diffusions such as Lévy flights.

Coalescing stochastic processes in retrival from semantic memory

Pierre-Yves QueauWojbor A. WoyczyńskiAlan J. Lerner — 2015

Mathematica Applicanda

Semantic memory retrieval is one of the most fundamental cognitive functions in humans. It is not fully understood and researchers from various fields of science struggle to find a model that would correlate well with experimental results and help understanding the complex background processes involved. To study such a phenomenon we need a relevant experimental protocol which can isolate the basic cognitive functions of interest from other perturbations. A variety of existing medical tests can provide...

A Lost Opportunity: Recovering the End of Major League Baseball's 1994 Strike Shortened Season

Zachary HassWojbor A. WoyczyńskiChris YanoskoEric Becker — 2012

Mathematica Applicanda

The 1994 Major League Baseball (MLB) Season ended prematurely when the players went on strike on August 12th, due to a labor disagreement with team owners. This paper describes the model estimation for predicting the runs scored in each of the unplayed games and gives the results of 1,000 simulations. Of particular interest are the Cleveland Indians and the Montreal Expos. The Expos were on pace to have the best season in franchise history (and the best record in the league), while the Indians were...

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