On the Range of Exponential Functionals of Levy Processes

被引：5
|
作者：
Behme, Anita [1 ,2 ]
Lindner, Alexander [3 ,4 ]
Maejima, Makoto [5 ]
机构：
[1] Tech Univ Dresden, Inst Math Stochast, D-01062 Dresden, Germany
[2] Tech Univ Munich, Zentrum Math, Boltzmannstr 3, D-85748 Garching, Germany
[3] Tech Univ Carolo Wilhelmina Braunschweig, Inst Math Stochast, D-38106 Braunschweig, Germany
[4] Univ Ulm, Inst Math Finance, D-89081 Ulm, Germany
[5] Keio Univ, Dept Math, Yokohama, Kanagawa 2238522, Japan
来源：
SEMINAIRE DE PROBABILITES XLVIII | 2016年 / 2168卷
基金：
日本学术振兴会;
关键词：
DISTRIBUTIONS; INTEGRALS;
D O I：
10.1007/978-3-319-44465-9_10
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We characterize the support of the law of the exponential functional integral(infinity)(0) e(-xi s-) d eta(s) of two one-dimensional independent Levy processes xi and eta. Further, we study the range of the mapping Phi(xi) for a fixed Levy process xi, which maps the law of eta(1) to the law of the corresponding exponential functional integral(infinity)(0)e(-xi s-) d eta(s). It is shown that the range of this mapping is closed under weak convergence and in the special case of positive distributions several characterizations of laws in the range are given.
引用
收藏
页码：267 / 303
页数：37
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