Galves A., Schmitt B.
Inequalities for hitting times in mixing dynamical systems
(30K, Plain TeX)
ABSTRACT. We prove that a hitting time of a mixing dynamical system can be sharply
approximated by an exponential random variable. More precisely, we prove that
there exists four strictly positive constants $ {\Lambda}_1, {\Lambda}_2,
\beta $, and $C$, such that, if $A$ is a cylinder and $\ta$ is the first time
the system visits $A$, then the following uniform upper bound holds
$$
\sup_{t > 0} \left\vert \P\left\{\ta > {t \over {\lambda(A) \pa}}\right\}
- e^{\displaystyle{- t}} \right\vert \le C \P(A)^{\beta} \ ,
$$
where $\pa$ is the probability of $A$ and $ \lambda(A) \in \left[\Lambda_1,