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Ergodicity and Law-of-large numbers for the Volterra Cox-Ingersoll-Ross process

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  • Mohamed Ben Alaya
  • Martin Friesen
  • Jonas Kremer

Abstract

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 $L^p$(\Omega)$ 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.

Suggested Citation

  • Mohamed Ben Alaya & Martin Friesen & Jonas Kremer, 2024. "Ergodicity and Law-of-large numbers for the Volterra Cox-Ingersoll-Ross process," Papers 2409.04496, arXiv.org.
    • Handle: RePEc:arx:papers:2409.04496
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    References listed on IDEAS

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