On the weak convergence of conditioned Bessel bridges
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917650601345024 |
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| author | Ishitani, Kensuke Rin, Tokufuku Yanashima, Shun |
| author_facet | Ishitani, Kensuke Rin, Tokufuku Yanashima, Shun |
| contents | 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 $t=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_11328 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the weak convergence of conditioned Bessel bridges Ishitani, Kensuke Rin, Tokufuku Yanashima, Shun Probability Primary 60F17, Secondary 60J25 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 $t=1$. |
| title | On the weak convergence of conditioned Bessel bridges |
| topic | Probability Primary 60F17, Secondary 60J25 |
| url | https://arxiv.org/abs/2201.11328 |