On some transformations between positive self-similar Markov processes

被引：6

作者：

Chaumont, Loic ^{[1
]}

Rivero, Victor ^{[2
,3
]}

机构：

[1] Univ Paris 06, Lab Probabil & Modeles Aleatoires, F-75252 Paris 05, France

[2] CIMAT AC, Dept Probabil & Stat, Guanajuato 36240, Gto, Mexico

[3] Univ Paris 10, F-92001 Nanterre, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2007年 / 117卷 / 12期

关键词：

self-similar Markov processes; Levy processes; weak convergence; decomposition at the minimum; conditioning; h-transforms;

D O I：

10.1016/j.spa.2007.03.007

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：

A path decomposition at the infimum for positive self-similar Markov processes (pssMp) is obtained. Next, several aspects of the conditioning to hit 0 of a pssMp are studied. Associated to a given pssMp X, that never hits 0, we construct a pssMp X down arrow that hits 0 in a finite time. The latter can be viewed as X conditioned to hit 0 in a finite time, and we prove that this conditioning is determined by the pre-minimum part of X. Finally, we provide a method for conditioning a pssMp that hits 0 by a jump to do it continuously. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：1889 / 1909

页数：21

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