The Annals of Probability

Asymptotics for hitting times

M. Kupsa and Y. Lacroix

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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.

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

First available in Project Euclid: 3 March 2005

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Primary: 37A05: Measure-preserving transformations 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 60F05: Central limit and other weak theorems 28D05: Measure-preserving transformations

Asymptotic distribution entrance hitting times Kac


Kupsa, M.; Lacroix, Y. Asymptotics for hitting times. Ann. Probab. 33 (2005), no. 2, 610--619. doi:10.1214/009117904000000883.

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