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March 2005 Asymptotics for hitting times
M. Kupsa, Y. Lacroix
Ann. Probab. 33(2): 610-619 (March 2005). DOI: 10.1214/009117904000000883

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.

Citation

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M. Kupsa. Y. Lacroix. "Asymptotics for hitting times." Ann. Probab. 33 (2) 610 - 619, March 2005. https://doi.org/10.1214/009117904000000883

Information

Published: March 2005
First available in Project Euclid: 3 March 2005

zbMATH: 1065.37006
MathSciNet: MR2123204
Digital Object Identifier: 10.1214/009117904000000883

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

Keywords: asymptotic distribution , entrance , hitting , Kac , times

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 2 • March 2005
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