楊朝強(qiáng)，常迎香

(蘭州交通大學(xué)數(shù)理與軟件工程學(xué)院，甘肅蘭州 730070)

一個(gè)具有反射壁的隨機(jī)環(huán)境中二重隨機(jī)游動(dòng)的注記

楊朝強(qiáng)，常迎香

(蘭州交通大學(xué)數(shù)理與軟件工程學(xué)院，甘肅蘭州 730070)

對(duì)一類隨機(jī)環(huán)境中的二重隨機(jī)游動(dòng)的首達(dá)概率進(jìn)行研究.在平穩(wěn)遍歷條件下討論了隨機(jī)環(huán)境中的單邊二重隨機(jī)游動(dòng)的常返性，應(yīng)用隨機(jī)環(huán)境下轉(zhuǎn)移概率的 Markov性，得出了在獨(dú)立同分布條件下的一個(gè)中心極限定理.

隨機(jī)環(huán)境；單邊二重隨機(jī)游動(dòng)；轉(zhuǎn)移概率；中心極限定理

近年來，隨機(jī)環(huán)境中的隨機(jī)游動(dòng)問題受到國(guó)內(nèi)外學(xué)者的廣泛關(guān)注[1-7]，尤其是在一些特殊環(huán)境下的隨機(jī)游動(dòng)，在滿足平穩(wěn)遍歷條件時(shí)，其轉(zhuǎn)移概率的分布往往會(huì)表現(xiàn)出一些優(yōu)良的極限性質(zhì).例如，文獻(xiàn)[8-9]引入了隨機(jī)環(huán)境中的單邊二重隨機(jī)游動(dòng)，在常返狀態(tài)下，考慮了游動(dòng)的首達(dá)時(shí)與分支鏈轉(zhuǎn)移概率所滿足的大數(shù)定律.本文繼續(xù)沿用文獻(xiàn)[8-9]中的二重隨機(jī)游動(dòng)模型，在平穩(wěn)遍歷條件下討論了游動(dòng)狀態(tài)的常返性，考慮了隨機(jī)環(huán)境下首達(dá)概率的Markov性，得出了在獨(dú)立同分布條件下的一個(gè)中心極限定理.

1 一些常返性結(jié)果

2 主要結(jié)論

[1]Kozlov M V. Random walk in a one dimensional random medium [J]. Theory of Probability and Its Applications, 1973, 18: 387-388.

[2]Solomon F. Random walk in a random environment [J]. The Annals of Probability, 1975, 3(1): 1-31.

[3]Szase D, Toth B. Peresist random walks in one-dimensional random environment [J]. Journal of Statistical Physics, 1984, 37(1): 28-38.

[4]Karlin S, Taylor H M. A First Course in Stochastic Processes [M]. New York: Academic Press, 1975: 474-489.

[5]Alili S. Persistent random walks in stationary environment [J]. Journal of Statistical Physics, 1999, 94(3): 469-494.

[6]基赫曼 N N, 斯科羅霍德 A B. 隨機(jī)過程論: 第一卷[M]. 石北源, 譯. 北京: 科學(xué)出版社, 1986: 125-127.

[7]Fayolle G, Malyshev V, Menshikov M V. Topics in the Constructive Theory of Countable Markov Chains [M]. Cambridge: Cambridge University Press, 1995: 98-130.

[8]王偉剛, 胡迪鶴. 隨機(jī)環(huán)境下單邊二重隨機(jī)游動(dòng)[J]. 工程數(shù)學(xué)學(xué)報(bào), 2010, 27: 92-98.

[9]榮民希, 胡迪鶴, 孔凡秋. 隨機(jī)環(huán)境中單邊二重生滅鏈的常返性[J]. 武漢大學(xué)學(xué)報(bào): 理學(xué)版, 2007, (1): 13-17.

Note about Random Walks of Order 2 with Reflecting Barrier in Random Environment

YANG Zhaoqiang, CHANG Yingxiang
(School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou, China 730070)

In this paper, issue of the probabilities of arriving for the 1st time of a class of random walks of Order 2 in a random environment was studied. And recurrence criterion of the random walks of single side with order 2 was discussed under the condition of the stationary and ergodic. Finally, a centre limit theorem of the random walks was obtained under the condition of independent and identically distributed by using Markov of transition probability in a random environment.

Random Environment; Random Walk of Single Side with Order 2; Transition Probability; Centre Limit Theorem

(編輯：王一芳)

O211.62

A

1674-3563(2012)01-0011-06

10.3875/j.issn.1674-3563.2012.01.003 本文的PDF文件可以從xuebao.wzu.edu.cn獲得

2011-05-13

甘肅省教育廳科研項(xiàng)目(0804-10)

楊朝強(qiáng)(1984- )，男，甘肅通渭人，碩士研究生，研究方向：隨機(jī)過程及應(yīng)用