Asymptotics for hitting times

2005/03/29 by M. Kupsa, Y. Lacroix
Mathematics · #math.PR #msc:37A05 #msc:37A50 #msc:60F05 #msc:28D05.

paper · pdf · doi:10.1214/009117904000000883

published as Annals of Probability 2005, Vol. 33, No. 2, 610-619 · 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)

arxiv created 2005/03/29 · arxiv updated 2009/12/01

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)6mmF=F:R→ [0,1]:\lbrack \matrixF is increasing, null on ]-∞, 0]; \noalignF is continuous and concave; \noalignF(t)≤ t for t≥ 0... 6pt Note that all possible asymptotics are absolutely continuous.

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