Publication Date:
2019-12-06
Description:
In this article we study basic properties of random variables X, and their associated distributions, in the second chaos, meaning that X has a representation X = ∑ k ≥ 1 λ k ( ξ k 2 - 1 ) , where ξ k ∼ N ( 0 , 1 ) are independent. We compute the Lévy-Khintchine representations which we then use to study the smoothness of each density function. In particular, we prove the existence of a smooth density with asymptotically vanishing derivatives whenever λ k ≠ 0 infinitely often. Our work generalises some known results presented in the literature.
Electronic ISSN:
2073-8994
Topics:
Mathematics
Permalink