From Markov Jump Systems to Two Species Competitive Lotka-Volterra Equations with Diffusion  

作　　者：Xue Qiang WANG Li Jun BO Yong Jin WANG 

机构地区：[1]School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China [2]Department of Mathematics, Xidian University, Xi'an 710071, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第1期157-170,共14页数学学报（英文版）

基　　金：Supported by National Natural Science Foundations of China (No. 10871103)

摘　　要：In this paper, we start at a random evolution system on biological particles, which is described by a Markov jump system. Under a suitable scaling, we perform a proper approximation procedure. Then the so-called weak convergence of Markov processes and Martingales allow us to establish a （deterministic） two species competitive Lotka-Volterra equation.In this paper, we start at a random evolution system on biological particles, which is described by a Markov jump system. Under a suitable scaling, we perform a proper approximation procedure. Then the so-called weak convergence of Markov processes and Martingales allow us to establish a （deterministic） two species competitive Lotka-Volterra equation.

关 键 词：Markov jump system competitive Lotka-Volterra equation weak convergence 

分 类 号：O21[理学—概率论与数理统计]