Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations
Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations
复制标题
无限遍历变换占据时间反正弦定律的多射线推广
DOI：
10.1090/tran/7755
复制
发表时间：
2019
影响因子：
1.3
通讯作者：
Yano Kouji
中科院分区：
文献类型：
--
作者：
Sera Toru;Yano Kouji
在强分布收敛的意义下，我们证明了保持无限测度的遍历变换占用时间比的联合分布收敛到Lamperti广义反正弦分布的多维形式。我们的结果可以应用于区间映射和马尔可夫链。我们采用双重拉普拉斯变换方法，研究了多射线扩散的占据时间。我们还讨论了逆问题。参考文献
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. References