Convergence results for the Time-Changed fractional Ornstein-Uhlenbeck processes
| Autor: | Ascione, Giacomo, Mishura, Yuliya, Pirozzi, Enrica |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper we study some convergence results concerning the one-dimensional distribution of a time-changed fractional Ornstein-Uhlenbeck process. In particular, we establish that, despite the time change, the process admits a Gaussian limit random variable. On the other hand, we prove that the process converges towards the time-changed Ornstein-Uhlenbeck as the Hurst index $H \to 1/2^+$, with locally uniform convergence of one-dimensional distributions. Moreover, we also achieve convergence in the Skorohod $J_1$-topology of the time-changed fractional Ornstein-Uhlenbeck process as $H \to 1/2^+$ in the space of c\`adl\`ag functions. Finally, we exploit some convergence properties of mild solutions of a generalized Fokker-Planck equation associated to the aforementioned processes, as $H \to 1/2^+$. Comment: 24 pages |
| Databáze: | arXiv |
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