Local extinction in continuous-state branching processes with immigration

被引：10

作者：

Foucart, Clement ^{[1
]}

Bravo, Geronimo Uribe ^{[2
]}

机构：

[1] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Area Invest Cientif, Mexico City 04510, DF, Mexico

来源：

BERNOULLI | 2014年 / 20卷 / 04期

关键词：

continuous-state branching process; polarity; random cutout; zero set; REPRESENTATIONS; TIME; DECOMPOSITION;

D O I：

10.3150/13-BEJ543

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：

The purpose of this article is to observe that the zero sets of continuous-state branching processes with immigration (CBI) are infinitely divisible regenerative sets. Indeed, they can be constructed by the procedure of random cutouts introduced by Mandelbrot in 1972. We then show how very precise information about the zero sets of CBI can be obtained in terms of the branching and immigrating mechanism.

引用

页码：1819 / 1844

页数：26

共 34 条

[1] Changing the branching mechanism of a continuous state branching process using immigration [J].

Abraham, Romain ;

Delmas, Jean-Francois .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2009, 45 (01) :226-238

[2]

[Anonymous], 2006, INTRO LECT FLUCTUATI

[3]

[Anonymous], 1989, REGULAR VARIATION

[4]

Bertoin J., 1999, Subordinators: Examples and Applications. Lectures on Probability Theory and Statistics, V1717, P1, DOI 10.1007/978-3-540-48115-71

[5]

Bertoin J., 1996, LEVY PROCESSES CAMBR, V121

[6]

Bi H., 2013, TIME MRCA STATIONARY

[7]

BLUMENTHAL RM, 1961, J MATH MECH, V10, P493

[8]

BLUMENTHAL RM, 1962, ILLINOIS J MATH, V6, P308

[9]

Caballero ME, 2010, PROBAB MATH STAT-POL, V30, P1

[10] Ν-measure for continuous state branching processes and its application [J].

Chu, Weijuan ;

Ren, Yan-Xia .

FRONTIERS OF MATHEMATICS IN CHINA, 2011, 6 (06) :1045-1058

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