局部遍历随机环境下一个重伸缩过程收敛的结果

广西师范大学学报（自然科学版） ›› 2012, Vol. 30 ›› Issue (2): 66-70.

局部遍历随机环境下一个重伸缩过程收敛的结果

胡华

宁夏大学数学计算机学院,宁夏银川750021

收稿日期:2012-01-15 出版日期:2012-06-20 发布日期:2018-12-03
通讯作者: 胡华(1962—),男,宁夏中宁人,宁夏大学教授。E-mail:huhuanum@163.com
基金资助:
国家自然科学基金资助项目(61063020);宁夏自然科学基金资助项目(NZ1050);宁夏研究生教育创新计划项目(2010)

A Convergence Result of a Rescale Process Within Locally Ergodic Random Environment

HU Hua

School of Mathematics and Computer Science,Ningxia University,Yinchuan Ningxia 750021,China

Received:2012-01-15 Online:2012-06-20 Published:2018-12-03

摘要/Abstract

摘要： 考虑一个重伸缩过程(X^η,ε_t)_t≥0,假设｛η(x)｝_x∈Z是由局部遍历性的概率测度分布的,本文研究此过程当ε→0时的极限。证明了在局部遍历性分布条件下,对于R上的二阶连续可微函数f(X)和某个与η独立的齐次扩散函数a(X),这个重伸缩过程依分布μ_ε收敛到R上具有无穷小生成元ddXa(X)ddXf(X)的扩散过程。

关键词: 局部遍历性, 随机游动, 重伸缩过程, 无穷小生成元

Abstract: This paper considers a rescaled process (X^η,ε_t)_t≥0,and it's assumed that ｛η(x)｝_x∈Zis distributed by a locally ergodic probability measure.The limit of the rescaled process is studied as ε→0.It is proved that under local ergodicity distributions,the rescaled process converges in distribution μ_ε to the diffusion process on R with infinitesimal generator ddXa(X)ddXf(X),for second-order continuous differentiablefunction f(X) on R and a certain homogenized diffusion functiona(X) which is independent of η.

Key words: locally ergodic, random walk, rescaled process, infinitesimal generator

中图分类号:

O211.6

胡华. 局部遍历随机环境下一个重伸缩过程收敛的结果[J]. 广西师范大学学报（自然科学版）, 2012, 30(2): 66-70.

HU Hua. A Convergence Result of a Rescale Process Within Locally Ergodic Random Environment[J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(2): 66-70.

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