LEVY PROCESSES AND LEVY WHITE NOISE AS TEMPERED DISTRIBUTIONS

被引：16
|
作者：
Dalang, Robert C. [1 ]
Humeau, Thomas [1 ]
机构：
[1] Ecole Polytech Fed Lausanne, Inst Math, Stn 8, CH-1015 Lausanne, Switzerland
来源：
ANNALS OF PROBABILITY | 2017年 / 45卷 / 6B期
关键词：
Levy white noise; Levy process; Levy random field; tempered distribution; positive absolute moment; SHARP MARKOV PROPERTY;
D O I：
10.1214/16-AOP1168
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We identify a necessary and sufficient condition for a Levy white noise to be a tempered distribution. More precisely, we show that if the Levy measure associated with this noise has a positive absolute moment, then the Levy white noise almost surely takes values in the space of tempered distributions. If the Levy measure does not have a positive absolute moment of any order, then the event on which the Levy white noise is a tempered distribution has probability zero.
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页码：4389 / 4418
页数：30
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