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

共 46 条

[21] Mimicking self-similar processes [J].

Fan, Jie Yen ;

Hamza, Kais ;

Klebaner, Fima .

BERNOULLI, 2015, 21 (03) :1341-1360

[22] SOME SELF-SIMILAR PROCESSES RELATED TO LOCAL-TIMES [J].

SHIEH, NR .

STATISTICS & PROBABILITY LETTERS, 1995, 24 (03) :213-218

[23] Inversion, duality and Doob h-transforms for self-similar Markov processes [J].

Alili, Larbi ;

Chaumont, Loic ;

Graczyk, Piotr ;

Zak, Tomas .

ELECTRONIC JOURNAL OF PROBABILITY, 2017, 22

[24] MOMENTS OF PASSAGE TIMES AND ASYMPTOTIC BEHAVIOR OF INCREASING SELF-SIMILAR MARKOV PROCESSES [J].

Hu, Wei ;

Liu, Luqin .

ACTA MATHEMATICA SCIENTIA, 2015, 35 (06) :1426-1436

[25] On the exponential functional of Markov Additive Processes, and applications to multi-type self-similar fragmentation processes and trees [J].

Stephenson, Robin .

ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2018, 15 (02) :1257-1292

[26] ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF THE FRAGMENTATION EQUATION WITH SHATTERING: AN APPROACH VIA SELF-SIMILAR MARKOV PROCESSES [J].

Haas, Benedicte .

ANNALS OF APPLIED PROBABILITY, 2010, 20 (02) :382-429

[27] A JUMP-TYPE SDE APPROACH TO REAL-VALUED SELF-SIMILAR MARKOV PROCESSES [J].

Doering, Leif .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 367 (11) :7797-7836

[28] Covariance function of vector self-similar processes [J].

Lavancier, Frederic ;

Philippe, Anne ;

Surgailis, Donatas .

STATISTICS & PROBABILITY LETTERS, 2009, 79 (23) :2415-2421

[29] Apparent multifractality of self-similar Levy processes [J].

Zamparo, Marco .

NONLINEARITY, 2017, 30 (07) :2592-2611

[30] REAL SELF-SIMILAR PROCESSES STARTED FROM THE ORIGIN [J].

Dereich, Steffen ;

Doring, Leif ;

Kyprianou, Andreas E. .

ANNALS OF PROBABILITY, 2017, 45 (03) :1952-2003

← 1 2 3 4 5 →