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 {6pt} {-3mm}(A){6mm}F={F:R\to [0,1]:\left\lbrack \matrixF is increasing, null on ]-\infty, 0]; \noalignF is continuous and concave; \noalignF(t)\le t for t\ge 0.\right.}. {6pt} Note that all possible asymptotics are absolutely continuous.Comment: Published at http://dx.doi.org/10.1214/009117904000000883 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org