02-254 Abadi M.
Statistics and error terms of occurrence times in mixing processes (313K, ps) Jun 5, 02
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Abstract. We study the statistics of visits to a set with small measure in a stochastic process with different kinds of mixing properties. We prove an upper bound for the error when approximating the first return time law to a small set, with a mixture of an exponential law and a degenerated law at the origin. We also prove that once the process enter to the small set the law of the sojourn time in it can be approximated by a geometric law with parameter that depends only on the recurrence properties of the event. We also provide an expression for the error on this approximation. Finally, we prove an error term in the approximation of the number of visits in whole process to a small set that does not recur, to the Poisson law. We obtain also an approximation for the moments of this number of visits.

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