On Moments of Infinitely Divisible Distribution Functions

Wolfe, Stephen James

Ann. Math. Statist., Tome 42 (1971) no. 6, p. 2036-2043 / Harvested from Project Euclid

Résumé

Let $F(x)$ be an infinitely divisible distribution function with a Levy-Khintchine function $G(u)$ and let $p$ be any positive number. It is shown that $F(x)$ has an absolute moment of the $p$th order if and only if $G(u)$ has an absolute moment of the $p$th order, and $F(x)$ has an exponential moment of the $p$th order if and only if $G(u)$ has an exponential moment of the $p$th order. This result generalizes a theorem of J. M. Shapiro. Other related results are also obtained.

Publié le : 1971-12-14
Classification:

@article{1177693071,
     author = {Wolfe, Stephen James},
     title = {On Moments of Infinitely Divisible Distribution Functions},
     journal = {Ann. Math. Statist.},
     volume = {42},
     number = {6},
     year = {1971},
     pages = { 2036-2043},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177693071}
}

Wolfe, Stephen James. On Moments of Infinitely Divisible Distribution Functions. Ann. Math. Statist., Tome 42 (1971) no. 6, pp.  2036-2043. http://gdmltest.u-ga.fr/item/1177693071/