On the occupation time on the half line of pinned diffusion processes

The aim of the present paper is to generalize Uvy's result of the occupation time on the half line of pinned Brownian motion for pinned diffusion processes. An asymptotic behavior of the distribution function at the origin of the occupation time Gamma(+)(t) and limit theorem for the law of the fraction Gamma(+)(t)/t when t -> infinity are studied. An expression of the distribution function by the Riemann-Liouville fractional integral for pinned skew Bessel diffusion processes is also obtained. Krein's spectral theory and Tauberian theorem play important roles in the proofs.