Moments of occupation times on spider diffusion rays
The amount of time that a stochastic process spends within a given set (up to a certain time) is called an occupation time. A famous result is Lévy’s arcsine law for Brownian motion. In this talk, I will first focus on one-dimensional diffusions and present a recursive formula for the moments of the occupation time on the positive real numbers. In the case of skew Bessel processes, this leads to an explicit expression for the moments in the form of a finite polynomial of the two parameters of the process. The results can be extended to so-called “spider diffusions” living on a number of half-lines that meet at a common point (akin to Walsh’s Brownian motion on a finite number of rays).