Ergodicity and Law-of-large numbers for the Volterra Cox-Ingersoll-Ross process
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| Format: | Preprint |
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2024
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| _version_ | 1866916973714079744 |
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| author | Alaya, Mohamed Ben Friesen, Martin Kremer, Jonas |
| author_facet | Alaya, Mohamed Ben Friesen, Martin Kremer, Jonas |
| contents | We study the Volterra Volterra Cox-Ingersoll-Ross process on $\mathbb{R}_+$ and its stationary version. Based on a fine asymptotic analysis of the corresponding Volterra Riccati equation combined with the affine transformation formula, we first show that the finite-dimensional distributions of this process are asymptotically independent. Afterwards, we prove a law-of-large numbers in $L^p$(Ω)$ with $p \geq 2$ and show that the stationary process is ergodic. As an application, we prove the consistency of the method of moments and study the maximum-likelihood estimation for continuous and discrete high-frequency observations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_04496 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ergodicity and Law-of-large numbers for the Volterra Cox-Ingersoll-Ross process Alaya, Mohamed Ben Friesen, Martin Kremer, Jonas Probability Mathematical Finance We study the Volterra Volterra Cox-Ingersoll-Ross process on $\mathbb{R}_+$ and its stationary version. Based on a fine asymptotic analysis of the corresponding Volterra Riccati equation combined with the affine transformation formula, we first show that the finite-dimensional distributions of this process are asymptotically independent. Afterwards, we prove a law-of-large numbers in $L^p$(Ω)$ with $p \geq 2$ and show that the stationary process is ergodic. As an application, we prove the consistency of the method of moments and study the maximum-likelihood estimation for continuous and discrete high-frequency observations. |
| title | Ergodicity and Law-of-large numbers for the Volterra Cox-Ingersoll-Ross process |
| topic | Probability Mathematical Finance |
| url | https://arxiv.org/abs/2409.04496 |