局部遍历随机环境下一个重伸缩过程收敛的结果

Journal of Guangxi Normal University(Natural Science Edition) ›› 2012, Vol. 30 ›› Issue (2): 66-70.

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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

Abstract

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

CLC Number:

O211.6

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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