- 02-254 Abadi M.
- Statistics and error terms of occurrence times in mixing processes
Jun 5, 02
(auto. generated ps),
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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
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
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