A joint limit theorem for compactly regenerative ergodic transformations
Volume 203 / 2011
Studia Mathematica 203 (2011), 33-45
MSC: Primary 28D05; Secondary 37A40, 37A50, 60G10, 37C30.
DOI: 10.4064/sm203-1-2
Abstract
We study conservative ergodic infinite measure preserving transformations satisfying a compact regeneration property introduced by the second-named author in J. Anal. Math. 103 (2007). Assuming regular variation of the wandering rate, we clarify the asymptotic distributional behaviour of the random vector $(Z_{n},S_{n})$, where $Z_{n}$ and $S_{n}$ are respectively the time of the last visit before time $n$ to, and the occupation time of, a suitable set $Y$ of finite measure.
