MPEJ Volume 7, No. 2, 19 pp.
Received: Jun 13, 2000. Revised: Oct 3, 2001. Accepted: Oct 9, 2001.
M. Abadi:
Exponential approximation for hitting times in mixing processes
ABSTRACT: We present bounds for the error of the exponential
approximation of the first occurrence time of a rare event in a
stationary stochastic process with a finite alphabet with the
$\alpha$-mixing property with a summable function $\alpha$ or with a
general $\phi$-mixing property. We prove a lower bound for this error
in terms of the measure of the cylinder and an upper bound as a
function of the measure of the cylinder plus the decay of correlation
of the process.