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

In this article, for some $d-$dimensional Gaussian processes \[X=\{X_t=(X^1_t,⋯,X^d_t):t≥0\},\] 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.