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

2024/09/06 by Mohamed Ben Alaya, Martin Friesen, Alaya, Mohamed Ben +3
Economics, Econometrics and Finance · #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2409.04496

openalex publication_date 2024/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Volterra Volterra Cox-Ingersoll-Ross process on 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 ≥ 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.

Related

• Local asymptotic properties for Cox-Ingersoll-Ross process with discrete observations
• Volterra square-root process: Stationarity and regularity of the law
• Infinite Dimensional Pathwise Volterra Processes Driven by Gaussian Noise -- Probabilistic Properties and Applications
• Sharp large deviations for the drift parameter of the explosive Cox-Ingersoll-Ross process
• The running maximum of the Cox-Ingersoll-Ross process with some properties of the Kummer function