Birth-death processes are time-changed Feller's Brownian motions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908465768693760 |
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| author | Li, Liping |
| author_facet | Li, Liping |
| contents | A Feller's Brownian motion is a diffusion process on the half-line with general boundary behavior at the origin, described by four parameters. A birth-death process, on the other hand, is a continuous-time Markov chain on the nonnegative integers, characterized by three parameters reflecting its behavior at infinity. This paper aims to build a connection between the two: we show that any Feller's Brownian motion can be transformed into a birth-death process via a specific time change, and vice versa. The transformation identifies a precise correspondence between their parameters. Our approach is based on a pathwise representation of the Feller process and offers a constructive framework for birth-death processes, filling a gap in the existing literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Birth-death processes are time-changed Feller's Brownian motions Li, Liping Probability A Feller's Brownian motion is a diffusion process on the half-line with general boundary behavior at the origin, described by four parameters. A birth-death process, on the other hand, is a continuous-time Markov chain on the nonnegative integers, characterized by three parameters reflecting its behavior at infinity. This paper aims to build a connection between the two: we show that any Feller's Brownian motion can be transformed into a birth-death process via a specific time change, and vice versa. The transformation identifies a precise correspondence between their parameters. Our approach is based on a pathwise representation of the Feller process and offers a constructive framework for birth-death processes, filling a gap in the existing literature. |
| title | Birth-death processes are time-changed Feller's Brownian motions |
| topic | Probability |
| url | https://arxiv.org/abs/2408.09364 |