The Lamperti representation of real-valued self-similar Markov processes

被引：36

作者：

Chaumont, Loic ^{[1
]}

Panti, Henry ^{[2
]}

Rivero, Victor ^{[2
]}

机构：

[1] Univ Angers, Dept Math, LAREMA, F-49045 Angers 01, France

[2] Ctr Invest Matemat CIMAT AC, Guanajuato 36240, Mexico

来源：

BERNOULLI | 2013年 / 19卷 / 5B期

关键词：

Lamperti representation; Levy processes; multiplicative invariant processes; self-similar Markov processes; LEVY PROCESSES;

D O I：

10.3150/12-BEJ460

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：

In this paper, we obtain a Lamperti type representation for real-valued self-similar Markov processes, killed at their hitting time of zero. Namely, we represent real-valued self-similar Markov processes as time changed multiplicative invariant processes. Doing so, we complete Kiu's work [Stochastic Process. Appl. 10 (1980) 183-191], following some ideas in Chybiryakov [Stochastic Process. Appl. 116 (2006) 857-872] in order to characterize the underlying processes in this representation. We provide some examples where the characteristics of the underlying processes can be computed explicitly.

引用

页码：2494 / 2523

页数：30

共 37 条

[31] SOME SELF-SIMILAR PROCESSES RELATED TO LOCAL-TIMES
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STATISTICS & PROBABILITY LETTERS, 1995, 24 (03) : 213 - 218
[32] ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF THE FRAGMENTATION EQUATION WITH SHATTERING: AN APPROACH VIA SELF-SIMILAR MARKOV PROCESSES
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[33] Self-similar scaling limits of non-increasing Markov chains
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ALBIN, JMP
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1992, 41 (01) : 1 - 31
[36] ON THE EXACT ASYMPTOTICS OF EXIT TIME FROM A CONE OF AN ISOTROPIC α-SELF-SIMILAR MARKOV PROCESS WITH A SKEW-PRODUCT STRUCTURE
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[37] Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Levy processes
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ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2009, 45 (03): : 667 - 684

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