Abstract
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≥1λk(ξ2k−1) , where ξk∼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 λk≠0 infinitely often. Our work generalises some known results presented in the literature.
Original language | English |
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Article number | 1487 |
Journal | SYMMETRY |
Volume | 11 |
Issue number | 12 |
DOIs | |
Publication status | Published - 2019 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Infinitely divisible distribution
- Second chaos
- Smooth density
- Symmetrised distributions