Derivatives of local times for some Gaussian fields II

Abstract: Given a $(2,d)$-Gaussian field [ Z=\big{ Z(t,s)= X^{H_1}_t -\tilde{X}^{H_2}_s, s,t \ge 0\big}, ] where $X^{H_1}$ and $\tilde{X}^{H_2}$ are independent $d$-dimensional centered Gaussian processes satisfying certain properties, we will give the necessary condition for existence of derivatives of the local time of $Z$.