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

被引：5

作者：

Wang, Xue Qiang ^{[1
,3
]}

Bo, Li Jun ^{[2
]}

Wang, Yong Jin ^{[1
,3
]}

机构：

[1] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[2] Xidian Univ, Dept Math, Xian 710071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2009年 / 25卷 / 01期

关键词：

Markov jump system; competitive Lotka-Volterra equation; weak convergence; CHEMICAL-REACTIONS; LIMIT-THEOREMS; MODEL;

D O I：

10.1007/s10114-008-5587-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：157 / 170

页数：14

共 16 条

[1]

Adams RA, 1978, Pure and applied mathematics, V65

[2] DETERMINISTIC LIMIT OF THE STOCHASTIC-MODEL OF CHEMICAL-REACTIONS WITH DIFFUSION [J].

ARNOLD, L ;

THEODOSOPULU, M .

ADVANCES IN APPLIED PROBABILITY, 1980, 12 (02) :367-379

[3]

Blount D, 1996, ANN PROBAB, V24, P639

[4] COMPARISON OF STOCHASTIC AND DETERMINISTIC MODELS OF A LINEAR CHEMICAL-REACTION WITH DIFFUSION [J].

BLOUNT, D .

ANNALS OF PROBABILITY, 1991, 19 (04) :1440-1462

[5]

BLOUNT D., 1992, Ann. Appl. Probab., V2, P131

[6]

Either S., 1986, Markov Processes: Characterization and Convergence

[7]

Gugg D., 2004, Stoch. Dyn, V4, P245

[8]

Han HD, 2005, J COMPUT MATH, V23, P449

[9] HIGH-DENSITY LIMIT-THEOREMS FOR NONLINEAR CHEMICAL-REACTIONS WITH DIFFUSION [J].

KOTELENEZ, P .

PROBABILITY THEORY AND RELATED FIELDS, 1988, 78 (01) :11-37

[10]

Kouritzin MA, 2002, ANN APPL PROBAB, V12, P1039

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