English

Which Urbanik class $L_k$, do the hyperbolic and the generalized logistic characteristic functions belong to?

Probability 2022-12-01 v1 Classical Analysis and ODEs

Abstract

Selfdecomposable variables obtained from series of Laplace (double exponential) variables are objects of this study. We proved that hyperbolic-sine and hyperbolic-cosine variables are in the difference of the Urbanik classes L2L_2 and L3L_3 while generalized logistic variable is at least in the Urbanik class L1L_1. Hence some ratios of those corresponding selfdecomposable characteristic functions are again selfdecomposable.

Keywords

Cite

@article{arxiv.2211.17064,
  title  = {Which Urbanik class $L_k$, do the hyperbolic and the generalized logistic characteristic functions belong to?},
  author = {Zbigniew J. Jurek},
  journal= {arXiv preprint arXiv:2211.17064},
  year   = {2022}
}