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Filtered data based estimators for stochastic processes driven by colored noise

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  • Pavliotis, Grigorios A.
  • Reich, Sebastian
  • Zanoni, Andrea

Abstract

We consider the problem of estimating unknown parameters in stochastic differential equations driven by colored noise, which we model as a sequence of Gaussian stationary processes with decreasing correlation time. We aim to infer parameters in the limit equation, driven by white noise, given observations of the colored noise dynamics. We consider both the maximum likelihood and the stochastic gradient descent in continuous time estimators, and we propose to modify them by including filtered data. We provide a convergence analysis for our estimators showing their asymptotic unbiasedness in a general setting and asymptotic normality under a simplified scenario.

Suggested Citation

  • Pavliotis, Grigorios A. & Reich, Sebastian & Zanoni, Andrea, 2025. "Filtered data based estimators for stochastic processes driven by colored noise," Stochastic Processes and their Applications, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:spapps:v:181:y:2025:i:c:s0304414924002667
    DOI: 10.1016/j.spa.2024.104558
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    References listed on IDEAS

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    1. Sharrock, Louis & Kantas, Nikolas & Parpas, Panos & Pavliotis, Grigorios A., 2023. "Online parameter estimation for the McKean–Vlasov stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 481-546.
    2. Papavasiliou, A. & Pavliotis, G.A. & Stuart, A.M., 2009. "Maximum likelihood drift estimation for multiscale diffusions," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3173-3210, October.
    3. Mattingly, J. C. & Stuart, A. M. & Higham, D. J., 2002. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 185-232, October.
    4. Della Maestra, Laetitia & Hoffmann, Marc, 2023. "The LAN property for McKean–Vlasov models in a mean-field regime," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 109-146.
    5. Giuseppe Pesce & Austin McDaniel & Scott Hottovy & Jan Wehr & Giovanni Volpe, 2013. "Stratonovich-to-Itô transition in noisy systems with multiplicative feedback," Nature Communications, Nature, vol. 4(1), pages 1-7, December.
    6. Gailus, Siragan & Spiliopoulos, Konstantinos, 2017. "Statistical inference for perturbed multiscale dynamical systems," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 419-448.
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