稳定随机变量序列几何加权和的Chover重对数律

The Chover Law of the Iterated Logarithm for Random Geometric Series of Stable Distribution

设｛Ｘｎ，ｎ≥ ０｝是独立同分布的随机变量序列，其分布函数是一个对称的指数为 ａ（０＜ ａ＜ ２）的稳定分布·本文证明了依概率 １有 ｌｉｍ ｓｕｐβ－ｌ－｜（ ｌ－βα）１／α∑∞ ｎ＝０βｎＸｎ＝ｅｘｐ（１／α）·

Let {Xn, n≥0} be mutually indepenent random variables, identically distributed acording to the symmetric stable distribution with exponent α(0 <α < 2). With probability one we have lim supsβ- l(1 -βα)1/α∑∞n=0, exp (1/α).