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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations


Authors: Toru Sera and Kouji Yano
Journal: Trans. Amer. Math. Soc. 372 (2019), 3191-3209
MSC (2010): Primary 60F05; Secondary 28D05, 37A40
DOI: https://doi.org/10.1090/tran/7755
Published electronically: May 30, 2019
MathSciNet review: 3988607
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Abstract: We prove that the joint distribution of the occupation time ratios for ergodic transformations preserving an infinite measure converges to a multidimensional version of Lamperti’s generalized arcsine distribution, in the sense of strong distributional convergence. Our results can be applied to interval maps and Markov chains. We adopt the double Laplace transform method, which has been utilized in the study of occupation times of diffusions on multiray. We also discuss the inverse problem.


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Additional Information

Toru Sera
Affiliation: Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan

Kouji Yano
Affiliation: Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
MR Author ID: 712148

Received by editor(s): November 13, 2017
Received by editor(s) in revised form: July 3, 2018
Published electronically: May 30, 2019
Additional Notes: The second author was supported by JSPS-MAEDI Sakura program and KAKENHI 26800058 and was partially supported by KAKENHI 24540390 and KAKENHI 15H03624.
Article copyright: © Copyright 2019 American Mathematical Society