Exact convergence rates to derivatives of local time for some self-similar Gaussian processes

In this article, for some d-dimensional Gaussian processes =\Xₜ= (X¹ₜ, , Xᵈₜ): t0\, \ whose components are i. i. d. 1-dimensional self-similar Gaussian process with Hurst index H (0, 1), we consider the asymptotic behavior of approximation of its k-th derivatives of local time under certain mild conditions, where k= (k₁, , kd) and k_'s are non-negative real numbers. We will give a derivative version of the limit theorems for functional of Gaussian processes and use this result to get the asymptotic behaviors.