On the Joint Law of the Occupation Times for a Diffusion Process on Multiray

For a diffusion process on multiray, the joint law of the occupation times on rays is studied. Two important formulae, the generalized Williams formula and the double Laplace transform formula, are proved. A limit theorem for the joint law and a representation of the density function are also discussed. The proofs are based on Itô’s excursion theory for Markov processes.