On the weak convergence of conditioned Bessel bridges

Kensuke Ishitani; Tokufuku Rin; Shun Yanashima

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arXiv · 2201.11328

On the weak convergence of conditioned Bessel bridges

Kensuke Ishitani·Tokufuku Rin·Shun Yanashima

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Abstract

The purpose of this paper is to introduce the construction of a stochastic process called "$\delta$-dimensional Bessel house-moving" and its properties. We study the weak convergence of $\delta$-dimensional Bessel bridges conditioned from above, and we refer to this limit as $\delta$-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 $\delta$-dimensional Bessel house-moving is a $\delta$-dimensional Bessel process hitting a fixed point for the first time at $t=1$.

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Kensuke Ishitani, Tokufuku Rin, Shun Yanashima. 2022-01-27. On the weak convergence of conditioned Bessel bridges. https://arxiv.org/abs/2201.11328

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