Hermite rank, power rank and the generalized Weierstrass transform
  Using the theory of generalized Weierstrass transform, we show that the Hermite rank is identical to the power rank in the Gaussian case, and that an Hermite rank higher than one is unstable with respect to a level shift. 
Shuyang Bai, Murad S. Taqqu
math.PR math.ST stat.TH