唐 玲, 徐 懷

(1.安徽建筑工業(yè)學(xué)院數(shù)理系,合肥 230601; 2.安徽大學(xué)數(shù)學(xué)與計(jì)算科學(xué)學(xué)院,合肥 230039)

復(fù)平穩(wěn)隨機(jī)序列均值遍歷性的兩個(gè)充要條件

唐 玲1, 徐 懷2

(1.安徽建筑工業(yè)學(xué)院數(shù)理系,合肥 230601; 2.安徽大學(xué)數(shù)學(xué)與計(jì)算科學(xué)學(xué)院,合肥 230039)

遍歷性是平穩(wěn)隨機(jī)過(guò)程的一個(gè)核心問(wèn)題,在實(shí)踐中有重要的應(yīng)用.這里首先給出復(fù)平穩(wěn)序列均值遍歷性的一個(gè)等價(jià)定義,在此基礎(chǔ)上證明了復(fù)平穩(wěn)序列情形下均值遍歷性的兩個(gè)充要條件,并給出一個(gè)形式簡(jiǎn)單的推論,這些結(jié)果有助于深入的理解復(fù)平穩(wěn)過(guò)程的均值遍歷性,同時(shí)也為估計(jì)復(fù)平穩(wěn)過(guò)程的均值提供了一種簡(jiǎn)單高效的方法.

復(fù)平穩(wěn)序列;均值遍歷性;充要條件

下面我們首先給出復(fù)平穩(wěn)序列及復(fù)平穩(wěn)序列均值遍歷性的定義：

1 主要結(jié)論

由于下文的需要,我們首先指出以下事實(shí)[7]：

現(xiàn)在依次給出復(fù)平穩(wěn)序列均值遍歷性?xún)蓚€(gè)充要條件及證明.

2 結(jié)束語(yǔ)

均值遍歷性定理的重要性在于它從理論上給出以下的保證：一個(gè)平穩(wěn)過(guò)程,如果它是均值遍歷性,則只從一次試驗(yàn)所得到的樣本函數(shù),就可以簡(jiǎn)便的估計(jì)出該平穩(wěn)過(guò)程的均值.實(shí)際問(wèn)題中,要嚴(yán)格的驗(yàn)證平穩(wěn)過(guò)程是否滿(mǎn)足均值遍歷性條件是比較困難的,但均值遍歷性條件較寬,工程中所需的平穩(wěn)過(guò)程大多數(shù)都能滿(mǎn)足[2,8].

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[4] Wolfgang S.Two mean ergodic sample-path properties of the Poisson process[J].Journal ofTheoretical Probability,2007,11(1)：197-208.

[5] Huzii M.The survey for research of mean ergodicty to a stationary Gaussian process[J].Annals of the Institute of Statistical Mathematics,2008,52(4)：259-268.

[6] Michael B.Ergodic theorems for random clusters[J].Stochastic Processes and their Applications,2008,120(3)：296-305.

[7] Tam P K,Tan K K.A mean ergodic theorem on vector spaces[J].Applied Mathematics Letters,1999,12(8)：61 -64.

[8] 林元烈.應(yīng)用隨機(jī)過(guò)程[M].北京：清華大學(xué)出版社,2002：136-207.

Two Necessary and Sufficient Conditions of Mean Ergodicity about Compound Value Stationary Sequence

TA N G L ing1, XU Huai2
(1.Department of Mathematics,Anhui Institute of Architecture&Industry,Hefei 230601,China; 2.School of Mathematics,Anhui University,Hefei 230039,China)

Ergodicity is a important property of stationary stochastic processes and has extensive application in practice.first we show an equivalent defination of the mean ergodicity to compound-value stationary sequence;then the two sufficient and necessary conditions of mean ergodicity are proven and a widely used proposition is given in the end of article.The estimation of mean can be gotten affectivity.

compound value stationary sequence;mean ergodicity;necessary and sufficient condition

O211.6

A

1672-1454(2011)05-0052-04

2008-10-14;[修改日期]2008-12-19

2011年安徽省高校自然科學(xué)基金科研資助項(xiàng)目(KJ2011z056)