Remarks on ergodicity and invariant occupation measure in branching diffusions with immigration

被引：1
|
作者：
Höpfner, R
Löcherbach, E
机构：
[1] Univ Paris 12, UFR Sci & Technol, F-94010 Creteil, France
[2] Johannes Gutenberg Univ Mainz, Fachbereich Math & Informat 17, D-55099 Mainz, Germany
来源：
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2005年 / 41卷 / 06期
关键词：
diffusing particles; branching; immigration; spatial subcriticality; invariant occupation measure; invariant occupation density; resolvants; stochastic flows;
D O I：
10.1016/j.anihpb.2004.09.001
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：
We give a necessary and sufficient condition for ergodicity with finite invariant occupation measure for branching diffusions with immigration. We do not assume uniformly subcritial reproduction means. We discuss the structure of the invariant occupation measure and of its density. (c) 2005 Elsevier SAS. All rights reserved.
引用
收藏
页码：1025 / 1047
页数：23
相关论文
共 50 条
  • [1] Invariant measure for diffusions with jumps
    Menaldi, JL
    Robin, M
    APPLIED MATHEMATICS AND OPTIMIZATION, 1999, 40 (01): : 105 - 140
  • [2] Invariant Measure for Diffusions with Jumps
    J. -L. Menaldi
    M. Robin
    Applied Mathematics and Optimization, 1999, 40 : 105 - 140
  • [3] Invariant measure for diffusions with jumps
    Department of Mathematics, Wayne State University, MI 48202, United States
    不详
    Appl Math Optim, 1 (105-140):
  • [4] Exponential ergodicity of branching processes with immigration and competition
    Li, Pei-Sen
    Li, Zenghu
    Wang, Jian
    Zhou, Xiaowen
    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2025, 61 (01): : 350 - 384
  • [5] SOME REMARKS ON ERGODICITY AND INVARIANT MEASURES
    SCHWEIGER, F
    MICHIGAN MATHEMATICAL JOURNAL, 1975, 22 (02) : 181 - 187
  • [6] LAN and LAMN for systems of interacting diffusions with branching and immigration
    Löcherbach, E
    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2002, 38 (01): : 59 - 90
  • [7] Measure-valued immigration diffusions and generalized ornstein-uhlenbeck diffusions
    Li Zenghu
    Acta Mathematicae Applicatae Sinica, 1999, 15 (3) : 310 - 320
  • [8] MEASURE-VALUED BRANCHING DIFFUSIONS WITH SPATIAL INTERACTIONS
    PERKINS, E
    PROBABILITY THEORY AND RELATED FIELDS, 1992, 94 (02) : 189 - 245
  • [9] MEASURE-VALUED BRANCHING DIFFUSIONS WITH SINGULAR INTERACTIONS
    EVANS, SN
    PERKINS, EA
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1994, 46 (01): : 120 - 168
  • [10] Existence, uniqueness and ergodicity of Markov branching processes with immigration and instantaneous resurrection
    Li JunPing
    Chen AnYue
    SCIENCE IN CHINA SERIES A-MATHEMATICS, 2008, 51 (07): : 1266 - 1286
12345