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The Chover law of the iterated logarithm for random geometric series of stable distribution. (Chinese. English summary) Zbl 1009.60010

Summary: Let \(\{X_n, n\geq 0\}\) be mutually independent random variables, identically distributed according to the symmetric stable distribution with exponent \(\alpha\) \((0< \alpha< 2)\). With probability one we have \[ \limsup_{\beta\to 1^-}\Biggl|(1- \beta^\alpha)^{1/\alpha} \sum^\infty_{n=0} \beta^n X_n\Biggr|^{1/\log|\log(1- \beta^\alpha)|}= \exp(1/\alpha). \]

MSC:

60F05 Central limit and other weak theorems
60F15 Strong limit theorems
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