In this article, for some d-dimensional Gaussian processes \(\begin{aligned} X=\big \{X_t=(X^1_t,\ldots ,X^d_t):t\ge 0\big \}, \end{aligned}\) whose components are i.i.d. 1-dimensional self-similar Gaussian processes with Hurst index \(H\in (0,1)\) , we consider the asymptotic behavior of approximation of its \(\varvec{k}\) -th derivatives of local time under certain mild conditions, where \(\varvec{k}=(k_1,\ldots ,k_d)\) and \(k_\ell \) ’s are non-negative real numbers. We will prove limit theorems for functionals of Gaussian processes related to derivatives of local time and use this result to obtain the asymptotic behaviors.
