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|Type:||Artigo de periódico|
|Title:||Sharp Error Terms for Return Time Statistics under Mixing Conditions|
|Abstract:||We describe the statistics of repetition times of a string of symbols in a stochastic process. Denote by tau (A) the time elapsed until the process spells a finite string A and by S (A) the number of consecutive repetitions of A. We prove that, if the length of the string grows unboundedly, (1) the distribution of tau (A) , when the process starts with A, is well approximated by a certain mixture of the point measure at the origin and an exponential law, and (2) S (A) is approximately geometrically distributed. We provide sharp error terms for each of these approximations. The errors we obtain are point-wise and also allow us to get approximations for all the moments of tau (A) and S (A) . To obtain (1) we assume that the process is phi-mixing, while to obtain (2) we assume the convergence of certain conditional probabilities.|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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