Geodesic
Integral transforms with infinitely divisible kernels
Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 4, pp. 856-863

Voir la notice de l'article provenant de la source Math-Net.Ru

Given $r$ characteristic functions $f_1 (u), \ldots ,f_r (u)$, none of which is identically equal to one, it is shown that the integral transform $$ \int_0^\infty \cdots \int_0^\infty {\left( {\prod\limits_{j = 1}^r {fj(u_j )^{s_j } } } \right)\,dF(s_1 , \ldots ,s_r )} $$ of the joint distribution function $F$ of $r$ non-negative random variables can be defined over a nonempty domain of natural numbers and it uniquely determines $F$. This result is used to obtain the converse of a multivariate version of a transfer theorem due to Gnedenko and Fahim, thus extending a result of Szasz and Frajeris in the univariate case. An application is also made to Lévy processes.
Keywords: intergral transform, infinitely divisible, vector of random sums, the Lévy process. 
@article{TVP_1994_39_4_a18,
     author = {M. Finkelstein and S. Scheiberg and H. G. Tucker},
     title = {Integral transforms with infinitely divisible kernels},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {856--863},
     publisher = {mathdoc},
     volume = {39},
     number = {4},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1994_39_4_a18/}
}
TY  - JOUR
AU  - M. Finkelstein
AU  - S. Scheiberg
AU  - H. G. Tucker
TI  - Integral transforms with infinitely divisible kernels
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1994
SP  - 856
EP  - 863
VL  - 39
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1994_39_4_a18/
LA  - en
ID  - TVP_1994_39_4_a18
ER  - 
%0 Journal Article
%A M. Finkelstein
%A S. Scheiberg
%A H. G. Tucker
%T Integral transforms with infinitely divisible kernels
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1994
%P 856-863
%V 39
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1994_39_4_a18/
%G en
%F TVP_1994_39_4_a18
M. Finkelstein; S. Scheiberg; H. G. Tucker. Integral transforms with infinitely divisible kernels. Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 4, pp. 856-863. http://geodesic.mathdoc.fr/item/TVP_1994_39_4_a18/