论文标题
时间变化的分数Ornstein-Uhlenbeck过程的收敛结果
Convergence results for the Time-Changed fractional Ornstein-Uhlenbeck processes
论文作者
论文摘要
在本文中，我们研究了一些有关时间变化的分数Ornstein-Uhlenbeck过程的收敛结果。特别是，我们确定，尽管时间变化，但该过程仍接受高斯极限随机变量。另一方面，我们证明该过程将随着时间变化的Ornstein-uhlenbeck作为Hurst索引$ h \ to 1/2^+$，具有一维分布的本地融合。此外，我们还将在Càdlàg函数空间中的$ H \ to 1/2^+$中的Skorohod $ j_1 $ - $ j1 $ topogy（作为$ h \ to 1/2^+$）中的融合。最后，我们利用了与上述过程相关的广义fokker-planck方程的温和解决方案的一些收敛性能，为$ h \至1/2^+$。
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 càdlàg functions. Finally, we exploit some convergence properties of mild solutions of a generalized Fokker-Planck equation associated to the aforementioned processes, as $H \to 1/2^+$.
