2020/11/05 by Giacomo Ascione, Ascione, Giacomo, Yuliya Mishura +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #35R11 (Secondary) #60G22 (Primary) 60F17 #FOS: Mathematics #Fractional Differential Equations Solutions #Probability (math.PR) #Statistical Mechanics and Entropy #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2011.02733
openalex publication_date 2020/11/05 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/31
In this paper we study some convergence results concerning the\none-dimensional distribution of a time-changed fractional Ornstein-Uhlenbeck\nprocess. In particular, we establish that, despite the time change, the process\nadmits a Gaussian limit random variable. On the other hand, we prove that the\nprocess converges towards the time-changed Ornstein-Uhlenbeck as the Hurst\nindex H \→ 1/2+, with locally uniform convergence of one-dimensional\ndistributions. Moreover, we also achieve convergence in the Skorohod\nJ1-topology of the time-changed fractional Ornstein-Uhlenbeck process as H\n\→ 1/2+ in the space of c `adl `ag functions. Finally, we exploit some\nconvergence properties of mild solutions of a generalized Fokker-Planck\nequation associated to the aforementioned processes, as H \→ 1/2+.\n