Asymptotics for hitting times

Asymptotics for hitting times

M. Kupsa and Y. Lacroix

Source: Ann. Probab. Volume 33, Number 2 (2005), 610-619.

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

$\hspace*{-8mm}\mbox{(A)}\hspace*{6mm}\mathcal{F}=\left\{F\dvtx \mathbb{R}\to [0,1]\dvtx \left\lbrack \matrix{F\mbox{ is increasing, null on }]\!-\!\infty ,0];\hfill \cr\noalign{\vspace*{3pt}}F\mbox{ is continuous and concave;}\hfill \cr\noalign{\vspace*{3pt}}F(t)\le t\mbox{ for }t\ge 0.\hfill}\right.\right\}.$

Note that all possible asymptotics are absolutely continuous.

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Primary Subjects: 37A05, 37A50, 60F05, 28D05

Keywords: Asymptotic distribution; entrance; hitting; times; Kac

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1109868594
Digital Object Identifier: doi:10.1214/009117904000000883
Mathematical Reviews number (MathSciNet): MR2123204
Zentralblatt MATH identifier: 02164476

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