Tokufuku Rin

On the weak convergence of conditioned Bessel bridges

The purpose of this paper is to introduce the construction of a stochastic process called "$δ$-dimensional Bessel house-moving" and its properties. We study the weak convergence of $δ$-dimensional Bessel bridges conditioned from above, and we refer to this limit as $δ$-dimensional Bessel house-moving. Applying this weak convergence result, we give the decomposition formula for its distribution and the Radon-Nikodym density for the distribution of the Bessel house-moving with respect to the one of the Bessel process. We also prove that $δ$-dimensional Bessel house-moving is a $δ$-dimensional Bessel process hitting a fixed point for the first time at $t=1$.