Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/75489
Type: Artigo de periódico
Title: Sharp errors for point-wise Poisson approximations in mixing processes
Author: Abadi, M
Vergne, N
Abstract: We describe the statistics of the number of occurrences of a string of symbols in a stochastic process: taking a string A of length n, we prove that the number of visits to A up to time t, denoted by N(t), has approximately a Poisson distribution. We provide a sharp error for this approximation. In contrast to previous works which present uniform error terms based on the total variation distance, our error is point-wise. As a byproduct we obtain that all the moments of Nt are finite. Moreover, we obtain explicit approximations for all of them. Our result holds for processes that verify the phi-mixing condition. The error term is explicitly expressed as a function of the rate function phi and is easily computable.
Country: Inglaterra
Editor: Iop Publishing Ltd
Rights: fechado
Identifier DOI: 10.1088/0951-7715/21/12/008
Date Issue: 2008
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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