Abstract: Paul L\'evy's classical arcsine law states that the occupation time ratio of one-dimensional Brownian motion for the positive side is arcsine-distributed. The arcsine law has been generalized to a variety of classes of stochastic processes and dynamical systems. In this talk, we focus on interval maps with two or more IFPs (indifferent fixed points), and present a strong distributional limit theorem for the joint-law of the occupation times for neighborhoods of IFPs. The scaling limit is a multidimensional version of Lamperti's generalized arcsine distribution, which is the joint-law of occupation times of a skew Bessel diffusion processes moving on multiray. This talk is based on a joint work with Kouji Yano (Kyoto University).
Tue, 28/05/2019 - 14:00 to 15:00