On the weak convergence of conditioned Bessel bridges

TL;DR

This paper introduces a new stochastic process called Bessel house-moving, studies its weak convergence from conditioned Bessel bridges, and derives its distributional properties and relation to Bessel processes.

Contribution

It constructs the Bessel house-moving process, establishes its weak convergence, and provides explicit distributional and density formulas, advancing understanding of Bessel-related stochastic processes.

Findings

Established weak convergence of conditioned Bessel bridges to Bessel house-moving

Derived the distribution decomposition and Radon-Nikodym density formulas

Proved Bessel house-moving hits a fixed point at t=1 for the first time

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 $t=1$.