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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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