- 01-475 Abadi M.
- SHARP ERROR TERMS AND NECCESARY CONDITIONS
FOR EXPONENTIAL HITTING TIMES IN MIXING PROCESSES
Dec 17, 01
(auto. generated ps),
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Abstract. We prove an upper bound for the error in the exponential approximation
of the hitting time law of a rare event in $\alpha$-mixing processes
exponential decay, $\phi$-mixing
a summable function $\phi$ and for general $\psi$-mixing
processes with a finite alphabet. In the first case the bound
is uniform as a function of the measure of the event.
In the last two cases the bound depends also on the time scale $t$.
This allow us to get further statistical properties as the
ratio convergence of the expected hitting time and the expected return
A uniform bound is a consequence.
We present an example that shows that this bound is sharp.
We also prove that second moments are not necessary for
having the exponential law. Moreover, we prove a necessary
condition for having the exponential limit law.