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

We prove that the joint distribution of the occupation time ratios for ergodic transformations preserving an infinite measure converges in the sense of strong distribution convergence to Lamperti's generalized arcsine distribution. 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.