Proof(s) of the Lamperti representation of continuous-state branching processes

被引：44

作者：

Emilia Caballero, Ma. ^{[1
]}

Lambert, Amaury ^{[2
]}

Uribe Bravo, Geronimo ^{[3
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City, DF, Mexico

[2] Univ Paris 06, Lab Probabil & Modeles Aleatoires, Paris, France

[3] Univ Nacl Autonoma Mexico, Inst Invest Matemat Aplicadas & Sistemas, Dept Probabilidad & Estadist, Mexico City, DF, Mexico

来源：

PROBABILITY SURVEYS | 2009年 / 6卷

关键词：

Continuous-state branching processes; spectrally positive Levy processes; random time change; stochastic integral equations; Skorohod topology;

D O I：

10.1214/09-PS154

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：

This paper uses two new ingredients, namely stochastic differential equations satisfied by continuous-state branching processes (CSBPs), and a topology under which the Lamperti transformation is continuous, in order to provide self-contained proofs of Lamperti's 1967 representation of CSBPs in terms of spectrally positive Levy processes. The first proof is a direct probabilistic proof, and the second one uses approximations by discrete processes, for which the Lamperti representation is evident.

引用

页码：62 / 89

页数：28

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