Behavior of the Hermite sheet with respect to theHurst index

We consider a $d$-parameter Hermite process with Hurst index $\mathbf{H}=(H_1,..,H_d)\in {\left(\frac{1}{2},1\right)}^d$ and we study its limit behavior in distribution when the Hurst parameters $H_i,i=1,..,d$ (or a part of them) converge to $\frac{1}{2}$ and/or 1. The limit obtained is Gaussian (when at least one parameter tends to $\frac{1}{2}$) and non-Gaussian (when at least one-parameter tends to 1 and none converges to $\frac{1}{2}$).