LEVY PROCESSES AND LEVY WHITE NOISE AS TEMPERED DISTRIBUTIONS

被引：14

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.

引用

页码：4389 / 4418

页数：30

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