Kensuke Ishitani, Tokufuku Rin, Shun Yanashima
Published 2022-01-27Version 1
The purpose of this paper is to introduce the construction of a new stochastic process called "$\delta$-dimensional Bessel house-moving" and its properties. $\delta$-dimensional Bessel house-moving is a $\delta$-dimensional Bessel process hitting a fixed point at $t=1$ for the first time. We have two methods for the construction of this process: characterizing it using the first hitting time of a Bessel process and obtaining it as the weak limit of conditioned Bessel bridges. We also study sample path properties of this process and give the decomposition formula for its distribution.
Comments: 34 pages, 5 figures
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