RANDOM WALKS WITH HEAVY TAILS AND LIMIT THEOREMS FOR BRANCHING PROCESSES WITH MIGRATION AND IMMIGRATION

被引：6

作者：

Feng, Yaqin ^{[1
]}

Molchanov, Stanislav ^{[1
]}

Whitmeyer, Joseph ^{[1
]}

机构：

[1] Univ N Carolina, Dept Math & Stat, Charlotte, NC 28223 USA

来源：

STOCHASTICS AND DYNAMICS | 2012年 / 12卷 / 01期

关键词：

Heavy tails; branching process; limit theorems;

D O I：

10.1142/S0219493712003626

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 central result of this paper is the existence of limiting distributions for two classes of critical homogeneous-in-space branching processes with heavy tails spatial dynamics in dimension d = 2. In dimension d >= 3, the same results are true without any special assumptions on the underlying (non-degenerated) stochastic dynamics.

引用

页数：23

共 11 条

[1]

[Anonymous], 2016, Generalized functions. V. 3: Theory of differential equations

[2] Critical nonlinearity exponent and self-similar asymptotics for Levy conservation laws [J].

Biler, P ;

Karch, G ;

Woyczynski, WA .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2001, 18 (05) :613-637

[3] Averaging principle for a class of stochastic reaction-diffusion equations [J].

Cerrai, Sandra ;

Freidlin, Mark .

PROBABILITY THEORY AND RELATED FIELDS, 2009, 144 (1-2) :137-177

[4] STABLE LIMIT DISTRIBUTIONS FOR STRONGLY MIXING SEQUENCES [J].

DENKER, M ;

JAKUBOWSKI, A .

STATISTICS & PROBABILITY LETTERS, 1989, 8 (05) :477-483

[5]

Galton F, 1873, ED TIMES, V17

[6]

Gikhman II, 1974, Theory Stochastic Processes

[7]

Harris T., 1963, THEORY BRANCHING PRO

[8]

Jourdain B, 2008, ALEA-LAT AM J PROBAB, V4, P1

[9] Correlation functions and invariant measures in continuous contact model [J].

Kondratiev, Yuri ;

Kutoviy, Oleksandr ;

Pirogov, Sergey .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2008, 11 (02) :231-258

[10] On contact processes in continuum [J].

Kondratiev, Yuri ;

Skorokhod, Anatoli .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2006, 9 (02) :187-198

← 1 2 →