独立的无界随机变量和的概率不等式

基金项目: 国家自然科学基金资助项目(19661001);广东省自然科学基金资助项目(199989)

Probability Inequalities for Sums of Independent Unbounded Random Variables

1.
Department of Statistics, Guangdong Commercial College, Guangzhou 510320, P R China;
2.
Department of Finance, Guanghua School of Management, Peking University, Beijing 100871, P R China

摘要: 研究了在概率空间(Ω,T,P)上,独立的无界随机变量和尾部概率不等式,提出了一种用切割原始概率空间(Ω,T,P)的新型方法去处理独立的无界随机变量和。给出了独立的无界随机变量和的指数型概率不等式。作为结果的应用,一些有趣的例子被给出。这些例子表明:文中提出的方法和结果对研究独立的无界随机变量和的大样本性质是十分有用的。
- 概率指数不等式 /
- 无界随机变量 /
- 收敛
Abstract: The tail probability inequalities for the sum of independent undbounded random variables on a probability space(Ω,T,P) were studied and a new method was proposed to treat the sum of independent unbounded random variables by truncating the original probability space(Ω,T,P).The probability exponential inequalities for sums of independent unbounded random variables were given.As applications of the results,some interesting examples were given.The examples show that the method proposed in the paper and the results of the paper are guite useful in the study of the large sample properties of the sums of independent unbounded random variables.
- probability exponential inequality /
- unbounded random variables /
- convergence

[1]	Bennett G.Probability inequalities for the sum of independent random variables[J].Journal of the American Statistical Association,1962,57(1):33-45.
[2]	Hoeffding W.Probability inequalities for sums of bounded random variables[J].JASA,1963,58(1):13-30.
[3]	Uspensky J V.Introduction to Mathematical Probability[M].New York:McGrawHill,1937.
[4]	Pollard D.Convergence of Stochastic Processes[M],New York:Springer-Verlag,1984.
[5]	Dudley R M.A Course on Empirical Processes,Springer Lecture Notes in Mathematics[M],1097,New York:Springer-Verlag,1984.
[6]	Shorack G R,Wellner J A.Empirical Processes with Applications to Statistics[M].New York:Wiley,1986.
[7]	Chow Y S,Teicher H.Probability Theory[M].New York:Springer-Verlag,1988.
[8]	Stout W F.Almost Sure Convergence[M].New York:Academic Press,Inc,1974.