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arXiv · 2403.12610

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

Petr Čoupek·Pavel Kříž·Bohdan Maslowski
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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 (as well as the speed of convergence) 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.

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Petr Čoupek, Pavel Kříž, Bohdan Maslowski. 2024-03-19. Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes. https://arxiv.org/abs/2403.12610

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