Asymptotics for hitting times

Abstract

In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class $$\text{(A)}\qquad \mathcal{F}=\left\{F: \mathbb R\to [0,1]: \left\lbrack \matrix{ F\text{ is increasing, null on ]−∞,0];}\hfill \cr F\text{ is continuous and concave;}\hfill \cr F(t)\le t\text{ for }t\ge 0.\hfill}\right.\right\}.$$ Note that all possible asymptotics are absolutely continuous.