无穷遍历变换占时反正弦律的多射线推广
Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations
摘要：
我们证明了在强分布收敛意义下，遍历变换的占用时间比的联合分布收敛于Lamperti广义反正弦分布的多维版本.我们的结果可应用于区间映射和马尔可夫链。本文采用双拉普拉斯变换方法，并将其应用于多射线上扩散占据时的研究。我们还讨论了逆问题。
英文摘要：
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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