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Large Deviation for Supercritical branching processes with Immigration

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Acta Mathematica Sinica,English Series 2016年第8期32卷 893-900页

作者： Jing Ning LIU Mei ZHANG School of Mathematical Sciences Laboratory of Mathematics and Complex SystemsBeijing Normal University

In this paper, we study the large deviation for a supercritical branching process with immigration controlled by a sequence of non-negative integer-valued independently identical distributed random variables, improving the previous results for non immigration processes. We rely heavily on the detail description and limit property of the generating function of immigration processes.

关键词： Supercritical branching processes large deviation immigration

Survival Probability of Population-size-dependent branching processes in Random Environments

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Acta Mathematicae Applicatae Sinica 2016年第2期32卷 477-484页

作者： Shi-xia MA Xiao-yu XING School of Sciences Hebei University of Technology

The class of population-size-dependent branching processes in independent identically distributed random environments is investigated. Under the critical case and appropriate moment assumption, we establish an asympto... 详细信息

关键词： branching processes population-size-dependent processes random environments survival proba-bility

SOME PROPERTIES OF GALTON-WATSON branching processes IN VARYING ENVIRONMENTS

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Acta Mathematica Scientia 2010年第4期30卷 1105-1114页

作者：余旌胡许芳 Department of Mathematics School of Science Wuhan University of Technology State Key Laboratory of Software Engineering Wuhan University Wuhan Institute of Physics and Mathematics the Chinese Academy of Sciences Graduate School of the Chinese Academy of Sciences

This article deals with some properties of Galton-Watson branching processes in varying environments. A necessary and suffcient condition for relative recurrent state is presented, and a series of ratio limit properti... 详细信息

关键词： branching processes varying environments non-homogeneous relative recurrent transition probability ratio theorem

Uniform Cramer moderate deviations and Berry-Esseen bounds for a supercritical branching process in a random environment

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Frontiers of Mathematics in China 2020年第5期15卷 891-914页

作者： Xiequan FAN Haijuan HU Quansheng LIU Center for Applied Mathematics Tianjin UniversityTianjin 300072China School of Mathematics and Statistics Northeastern University at QinhuangdaoQinhuangdao 066004China Universite de Bretagne-Sud LMBAUMR CNRS 6205Campus de Tohannic56017 VannesFrance School of Statistics and Mathematics Zhongnan University of Economics and LawWuhan 430073China

Let{Zn,n≥0}be a supercritical branching process in an independent and identically distributed random environment.We prove Cramer moderate deviations and Berry-Esseen bounds for log(Zn+n0/Zn0)uniformly in n0∈N,which extend the corresponding results by I.Grama,Q.Liu,and M.Miqueu[Stochastic Process.Appl.,2017,127:1255-1281]established for n0=0.The extension is interesting in theory,and is motivated by applications.A new method is developed for the proofs;some conditions of Grama et al.are relaxed in our present setting.An example of application is given in constructing confidence intervals to estimate the criticality parameter in terms of log(Zn+n0/Zn0)and n.

关键词： branching processes random environment Cramer moderatedeviations Berry-Esseen bounds

Deviation Inequalities for a Supercritical branching Process in a Random Environment

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Journal of Mathematical Research with Applications 2022年第4期42卷 427-440页

作者： Huiyi XU Center for Applied Mathematics Tianjin University

Let {Z, n ≥ 0} be a supercritical branching process in an independent and identically distributed random environment ξ =(ξ). In this paper, we get some deviation inequalities for ln(Z/Z). And some applications are ... 详细信息

关键词： deviation inequalities branching processes random environment

Tanaka Formula and Local Time for a Class of Interacting branching Measure-valued Diffusions

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1059-1098页

作者： Donald A.DAWSON Jean VAILLANCOURT Hao WANG School of Mathematics and Statistics Carleton UniversityOttawaCanada Department of Decision Sciences HECMontrealCanada Department of Mathematics University of OregonEugeneUSA

We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),... 详细信息

关键词： Measure-valued diffusions stochastic partial differential equations superprocesses branching processes local time Tanaka formula