A note on the infinite divisibility of a class of transformations of   normal variables
  This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We relate our result with some known skewing mechanisms. 
A. Murillo-Salas and F. J. Rubio
math.ST stat.TH