This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of such transformations of normal variables which produces non-infinitely divisible distributions. We relate our result with some known skewing mechanisms.
"A note on the infinite divisibility of a class of transformations of normal variables." Braz. J. Probab. Stat. 27 (4) 601 - 607, November 2013. https://doi.org/10.1214/12-BJPS187