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B1953
Title: Ornstein - Uhlenbeck process driven by alpha-stable process and its Gamma subordination Authors:  Aleksandra Grzesiek - Wroclaw Univeristy of Science and Technology (Poland) [presenting]
Agnieszka Wylomanska - Wroclaw University of Science and Technology (Poland)
Janusz Gajda - University of Warsaw (Poland)
Abstract: The variety and diversity of phenomena surrounding us and easy access to empirical data require either new and more complicated models that allow capturing features to resemble the data. We study the Ornstein-Uhlenbeck (OU) process driven by the alpha-stable Levy process delayed by the Gamma subordinator. The considered model captures the essential features of the parent process, i.e., the OU process with heavy-tailed-based distribution; however, it also possesses some characteristics that are not adequate to the model without the subordination scenario. Thus, it can be beneficial for real data with very specific behavior. The considered model can be regarded as the natural extension of the variance Gamma process that arises as the ordinary Brownian motion time-changed by the Gamma process.