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Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes

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  • Čoupek, Petr
  • Kříž, Pavel
  • Maslowski, Bohdan

Abstract

In this paper, we study parameter identification for solutions to (possibly non-linear) SDEs driven by additive Rosenblatt process and singularity of the induced laws on the path space. We propose a joint estimator for the drift parameter, diffusion intensity, and Hurst index that can be computed from discrete-time observations with a bounded time horizon and we prove its strong consistency under in-fill asymptotics with a fixed time horizon. As a consequence of this strong consistency, singularity of measures generated by the solutions with different drifts is shown. This results in the invalidity of a Girsanov-type theorem for Rosenblatt processes.

Suggested Citation

  • Čoupek, Petr & Kříž, Pavel & Maslowski, Bohdan, 2025. "Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes," Stochastic Processes and their Applications, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:spapps:v:179:y:2025:i:c:s0304414924002072
    DOI: 10.1016/j.spa.2024.104499
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    References listed on IDEAS

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    1. Albin, J. M. P., 1998. "A note on Rosenblatt distributions," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 83-91, September.
    2. Obayda Assaad & Ciprian A. Tudor, 2020. "Parameter identification for the Hermite Ornstein–Uhlenbeck process," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 251-270, July.
    3. Bardet, J.-M. & Tudor, C.A., 2010. "A wavelet analysis of the Rosenblatt process: Chaos expansion and estimation of the self-similarity parameter," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2331-2362, December.
    4. Nourdin, Ivan & Diu Tran, T.T., 2019. "Statistical inference for Vasicek-type model driven by Hermite processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3774-3791.
    5. Kerchev, George & Nourdin, Ivan & Saksman, Eero & Viitasaari, Lauri, 2021. "Local times and sample path properties of the Rosenblatt process," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 498-522.
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