随机变量序列与指数分布序列的比较及若干强偏差定理

Comparison between arbitrary random sequence and exponential distribution and some strong deviation theorems

利用对数似然比作为一般非负连续型随机变量序列相对于服从指数分布的独立但不同分布随机变量序列偏差的一种随机性度量,运用鞅理论及分析方法,研究了一类随机变量序列加权和的用不等式表示的极限定理,即强偏差定理。

The notion of logarithmic likelihoo d ratio ,as a random measure of the deviation of a sequence of non-negative continuous random sequence from independent random sequence w ith exponential distribution,is in tro-duced.By using the martingale theory and analytic method ,some strong li mit theorems represented by inequality of weighted random sequence is studi ed ,i.e.strong deviation theorems.