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 $Z$.