无穷维线性反应扩散过程的极限状态  

Limit for Infinite dimensional linear reaction and diffusion processes

作　　者：郑晓阳[1] 徐润章[1] 赵军生[2] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001 [2]黑龙江大学理学院,黑龙江哈尔滨150080

出　　处：《哈尔滨工业大学学报》2006年第3期432-435,463,共5页Journal of Harbin Institute of Technology

基　　金：国家自然科学基金资助项目(10271034)

摘　　要：揭示了无穷维线性反应扩散过程和偏微分方程这两种描述反应扩散现象的基本工具的关系,证明了无穷维线性反应扩散过程的大数定理,给出了无穷维线性反应扩散过程的极限状态.讨论了当无穷维线性反应扩散过程的无穷小算子中的参数随指标n变化时,反应扩散过程依概率收敛于一偏微分方程的解的条件,揭示了此偏微分方程的系数与过程的无穷小算子中的参数之间的关系.The relation between infinite dimensional linear reaction and diffusion processes and partial differential equations as two basic tools for studying reaction and diffusion phenomenon is reuealed. A law of large number for infinite dimensional linear reaction and diffusion processes is proved, the limit of processes is obtained. We have proved that a series of infinite dimensional linear reaction and diffusion processes converges to a solution of a partial differential equation under some conditions, and reveals the relation between the coefficients of the partial differential equation and the parameters of infinitesimal operator of the processes.

关 键 词：无穷维线性反应扩散过程 马氏半群 无穷小算子 无穷质点马氏过程 反应扩散方程 

分 类 号：O211.6[理学—概率论与数理统计]