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Peer-reviewedCC BYStochastic Processes and their Applications

Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process

  • Mohamed Ben Alaya
  • Martin Friesen
  • Jonas Kremer
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Abstract

We investigate maximum likelihood estimation for the drift parameters of stochastic Volterra processes in the ergodic regime. In our first result, we establish the equivalence of laws under general changes of drift and provide the corresponding Radon-Nikodym derivative. This allows us to develop a rigorous maximum likelihood estimation framework. As an application, we study the Volterra Ornstein–Uhlenbeck process in the ergodic regime, considering both continuous-time and high-frequency discrete-time observations. In both regimes, we prove the consistency and asymptotic normality of the maximum likelihood estimators. A key intermediate result, which may be of independent interest, is a uniform Birkhoff-type theorem under an asymptotic independence condition. This theorem yields a locally uniform Law of Large Numbers over the parameter space.

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Cite

BibTeXRIS
BibTeX
@article{alaya2026maximum,
  title = {{Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process}},
  author = {Mohamed Ben Alaya and Martin Friesen and Jonas Kremer},
  journal = {Stochastic Processes and their Applications},
  year = {2026},
  month = oct,
  doi = {10.1016/j.spa.2026.104907},
  url = {https://hal.science/hal-05782878v1},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process
AU  - Mohamed Ben Alaya
AU  - Martin Friesen
AU  - Jonas Kremer
PY  - 2026
DA  - 2026/10/07
JO  - Stochastic Processes and their Applications
DO  - 10.1016/j.spa.2026.104907
UR  - https://hal.science/hal-05782878v1
AB  - We investigate maximum likelihood estimation for the drift parameters of stochastic Volterra processes in the ergodic regime. In our first result, we establish the equivalence of laws under general changes of drift and provide the corresponding Radon-Nikodym derivative. This allows us to develop a rigorous maximum likelihood estimation framework. As an application, we study the Volterra Ornstein–Uhlenbeck process in the ergodic regime, considering both continuous-time and high-frequency discrete-time observations. In both regimes, we prove the consistency and asymptotic normality of the maximum likelihood estimators. A key intermediate result, which may be of independent interest, is a uniform Birkhoff-type theorem under an asymptotic independence condition. This theorem yields a locally uniform Law of Large Numbers over the parameter space.
SN  - 0304-4149
SN  - 1879-209X
ER  -