Driven by Brownian motion Cox-Ingersoll-Ross and squared Bessel processes: interaction and phase transition
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| Format: | Preprint |
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2024
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| _version_ | 1866916442676396032 |
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| author | Mishura, Yuliya Ralchenko, Kostiantyn Kushnirenko, Svitlana |
| author_facet | Mishura, Yuliya Ralchenko, Kostiantyn Kushnirenko, Svitlana |
| contents | This paper studies two related stochastic processes driven by Brownian motion: the Cox-Ingersoll-Ross (CIR) process and the Bessel process. We investigate their shared and distinct properties, focusing on time-asymptotic growth rates, distance between the processes in integral norms, and parameter estimation. The squared Bessel process is shown to be a phase transition of the CIR process and can be approximated by a sequence of CIR processes. Differences in stochastic stability are also highlighted, with the Bessel process displaying instability, while the CIR process remains ergodic and stable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_13231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Driven by Brownian motion Cox-Ingersoll-Ross and squared Bessel processes: interaction and phase transition Mishura, Yuliya Ralchenko, Kostiantyn Kushnirenko, Svitlana Probability 60H10 This paper studies two related stochastic processes driven by Brownian motion: the Cox-Ingersoll-Ross (CIR) process and the Bessel process. We investigate their shared and distinct properties, focusing on time-asymptotic growth rates, distance between the processes in integral norms, and parameter estimation. The squared Bessel process is shown to be a phase transition of the CIR process and can be approximated by a sequence of CIR processes. Differences in stochastic stability are also highlighted, with the Bessel process displaying instability, while the CIR process remains ergodic and stable. |
| title | Driven by Brownian motion Cox-Ingersoll-Ross and squared Bessel processes: interaction and phase transition |
| topic | Probability 60H10 |
| url | https://arxiv.org/abs/2410.13231 |