Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar by Pavel Kriz and Petr Coupek: Rosenblatt Process - Parameter Estimation and Singularity of Laws
Speakers: Pavel Kriz and Petr Coupek, Department of Mathematics, Charles University, Prague, Czech Republic
Title: Rosenblatt Process - Parameter Estimation and Singularity of Laws
Abstract: The Rosenblatt process is a continuous self-similar process with stationary increments that has the same covariance structure as the fractional Brownian motion, but with non-Gaussian marginals from the second Wiener chaos. In this talk, we will briefly outline its construction and address some of its properties. Subsequently, we will address the problem of joint estimation of the Hurst parameter, noise intensity and drift intensity for discretely sampled solutions to (non)linear stochastic differential equations (SDEs) driven by an additive Rosenblatt process. We introduce consistent estimators on a fixed (and bounded) time interval with in-fill asymptotics. A surprising consequence of the existence of such estimators is the singularity of laws (on the path space) of solutions to the considered SDEs with different drift intensities even on bounded time intervals. This is in sharp contrast with SDEs driven by a (fractional) Brownian motion, where the Girsanov theorem guarantees equivalence of the laws on bounded intervals. The talk is based on the recent paper
https://doi.org/10.1016/j.spa.
Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar