譚成良,吳群英

(桂林工學(xué)院數(shù)理系,廣西桂林 541004)

ρ?混合隨機(jī)場(chǎng)強(qiáng)大數(shù)律的收斂速度

譚成良,吳群英

(桂林工學(xué)院數(shù)理系,廣西桂林 541004)

建立了ρ?混合隨機(jī)場(chǎng)的Rosenthal型最大值矩不等式和強(qiáng)大數(shù)律的收斂速度.所得結(jié)果改進(jìn)并且推廣了相關(guān)文獻(xiàn)中的結(jié)果.

ρ?混合隨機(jī)場(chǎng)；完全收斂性；強(qiáng)大數(shù)律

1 引言

2 引理及其證明

證明引理1的證明與文[7]中的引理A.2.證明類似.

3 定理及其證明

[1]Zhang L X,Wang X Y.Convergence rates in the strong law s of asym ptotically negatively associated random field[J].App l.Math.J.Chinese Univ.,Ser B,1999,14:406-416.

[2]U tev SP.M axim al inequalitiesand an invariance p rincip le for a classofweakly dependent random variables[J]. J.Theoet Ptobab,2003,(16):101-115.

[3]Zhang L X.A functional central lim it theorem for asym ptotically negatively dependent random variables[J]. Acta M ath.Hunger.,2000,86(3):237-259.

[4]Zhang L X.Wen JW.A weak convergence for negatively associated fields[J].Statst Probab Lett.,2001b,53:259-267.

[5]Ko M H,Kim T S,K im H C.Strong laws of large numbers for asym ptotically quadrant independent random fields[J].Comm Korean M ath.Soc.,2004,19:765-773.

[6]Cai G H.Moment inequalities and convergence rates in the strong laws forρ?-m ixing random fields[J].J. M ath.Chem.,2006,39(2):243-251.

[7]張立新,聞繼威.B值混合隨機(jī)場(chǎng)的強(qiáng)大數(shù)律[J],數(shù)學(xué)年刊:A輯,2001,22(2):205-216.

[8]吳群英.混合序列的概率極限理論[M].2006,北京:高等教育出版社.

Com plete convergence rates in the strong law sforρ?-mixing random fields

TAN Cheng-liang,WU Qun-ying

(Departm ent of Mathem atics and Physics,Guilin University of Technology,Guilin 541004,China)

By using a Rosenthal type inequality established there,the com p lete convergence rates in the strong law s forρ?-m ixing random fields are discussed.The result obtained extends the results of related papers.

ρ?-m ixing random fields,the law of large strong numbers,com p lete convergence

O211.4

A

1008-5513(2009)02-0402-06

2007-06-10.

國(guó)家自然科學(xué)基金(10661006),廣西研究生教育創(chuàng)新計(jì)劃項(xiàng)目(2007105960812M 18).

譚成良(1982-),碩士,研究方向：概率極限理論與計(jì)算數(shù)學(xué).

2000M SC:60F15