Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations
Probability
2018-11-19 v3 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1711.03260,
title = {Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations},
author = {Toru Sera and Kouji Yano},
journal= {arXiv preprint arXiv:1711.03260},
year = {2018}
}