On determining an infinitely divisible distribution function by its values on a~half-line
Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 2, pp. 393-399
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Theorem. {\it Let $F(x)$ be an infinitely divisible distribution function with characteristic function $f(t)$. Suppose $f$ is holomorphic in $\{\operatorname{Im} z>0\}$ ($\{\operatorname{Im} z0\}$). If an infinitely divisible distribution function $G$ coincides with $F$ on a half-line $(-\infty,a)$ (on a half-line $(a,\infty)$) then either $F(x)$ equals zero (equals one) on the half-line or $F(x)=G(x)$ for all $x$.}
The theorem generalizes a result of H. Rossberg [1]. Examples are given which show that the analiticity condition is essential.
@article{TVP_1977_22_2_a15,
author = {I. A. Ibragimov},
title = {On determining an infinitely divisible distribution function by its values on a~half-line},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {393--399},
publisher = {mathdoc},
volume = {22},
number = {2},
year = {1977},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_2_a15/}
}
TY - JOUR AU - I. A. Ibragimov TI - On determining an infinitely divisible distribution function by its values on a~half-line JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1977 SP - 393 EP - 399 VL - 22 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1977_22_2_a15/ LA - ru ID - TVP_1977_22_2_a15 ER -
I. A. Ibragimov. On determining an infinitely divisible distribution function by its values on a~half-line. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 2, pp. 393-399. http://geodesic.mathdoc.fr/item/TVP_1977_22_2_a15/