Polynomials in Gaussian variables and infinite divisibility? (English) Zbl 0533.60033

Rosenblatt, M.

Contributions to probability, Collect. Pap. dedic. E. Lukacs, 139-142 (1981).

Summary: [For the entire collection see Zbl 0527.00019.]
The following open problem in the study of infinitely divisible laws is mentioned and motivated: Let Y be a Gaussian random variable. Determine those polynomials in Y whose distribution is infinitely divisible.

MSC:

60F05	Central limit and other weak theorems
62E10	Characterization and structure theory of statistical distributions
60E07	Infinitely divisible distributions; stable distributions

Keywords:

asymptotic normality of U statistics; Gaussian random variable; infinite divisibility; Hermite polynomials

Citations:

Zbl 0527.00019