97-128 Galves A., Schmitt B.

Inequalities for hitting times in mixing dynamical systems (30K, Plain TeX) Mar 17, 97

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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,

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