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 to-wards the time-changed Ornstein–Uhlenbeck as the Hurst index H → 1/2+,with locally uniform convergence of one-dimensional distributions. Moreover, we also achieve convergence in the Skorokhod J1-topology of the time-changed fractional Ornstein–Uhlenbeck process as H → 1/2+ in the space of càdlàg functions. Finally, we exploit some convergence properties of mild solutions of a generalized Fokker– Planck equation associated to the aforementioned processes, as H → 1/2+.

Convergence results for the time-changed fractional ornstein–uhlenbeck processes

Ascione G.;Mishura Y.;Pirozzi E.
2021

Abstract

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 to-wards the time-changed Ornstein–Uhlenbeck as the Hurst index H → 1/2+,with locally uniform convergence of one-dimensional distributions. Moreover, we also achieve convergence in the Skorokhod J1-topology of the time-changed fractional Ornstein–Uhlenbeck process as H → 1/2+ in the space of càdlàg functions. Finally, we exploit some convergence properties of mild solutions of a generalized Fokker– Planck equation associated to the aforementioned processes, as H → 1/2+.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/868561
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