Higher-order Derivative Local Time for Fractional Ornstein-Uhlenbeck Processes

Abstract

In this article, existence of the $k$-th order derivatives of local time ${\hat{\alpha }}^{(k)}(x,t)$ is considered for two d-dimensional fractional Ornstein-Uhlenbeck processes $X_t^{H_1}$ and ${\tilde{X}}_s^{H_2}$ with Hurst parameters $H_1$ and $H_2$, respectively. Moreover, H$\hat{o}$lder regularity condition of fractional Ornstein-Uhlenbeck process $X_t^H$ of local time ${\tilde{\alpha }}^{(k)}(x,t)$ is obtained by some techniques using in Guo et al. (2017) and in Lou et al. (2017).

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