一类连续状态非线性分枝过程的离散逼近  

The discrete approximation of a class of continuous-state nonlinear branching processes

作　　者：李培森 杨叙 周晓文 Pei-Sen Li;Xu Yang;Xiaowen Zhou

机构地区：[1]中国人民大学数学科学研究院,北京100872 [2]北方民族大学数学与信息科学学院,银川750021 [3]Department of Mathematics and Statistics, Concordia University

出　　处：《中国科学：数学》2019年第3期403-414,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11771046;11731012和11771018);北方民族大学重大专项(批准号:ZDZX201804);宁夏高等学校一流学科建设(批准号:NXYLXK2017B09);Natural Sciences and Engineering Research Council of Canada(批准号:RGPIN-2016-06704)资助项目

摘　　要：本文考虑一类连续状态非线性分枝过程.直观上,这是一类带竞争且分枝速率与状态相依的连续状态分枝过程.我们可以用由Brown运动和Poisson随机测度驱动的随机微分方程的解来构造该类过程.本文的主要结果是构造一列离散状态Markov链,并在较弱的条件下,通过胎紧性结论以及构造无穷维乘积空间上的收敛序列的方法证明其在轨道空间上弱收敛于上述连续状态的非线性分枝过程.In this paper we consider a general continuous-state nonlinear branching process which can be identi-?ed as a nonnegative solution to a nonlinear version of the stochastic diffierential equation driven by Brownian motion and Poisson random measure.Intuitively,this process is a branching process with population-size-dependent branching rates and with competition.We construct a sequence of discrete-state nonlinear branching processes and prove that it converges weakly to the continuous-state nonlinear branching process by using tightness arguments and convergence criteria on in?nite-dimensional space.

关 键 词：分枝过程 非线性分枝 随机微分方程 胎紧性 

分 类 号：O211.65[理学—概率论与数理统计]