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The law of the iterated logarithm for the last exit time of independent random sequences

  • J. Hüsler
Article

Summary

Let tβ=max{k ≧0:X k k} if such a k exists and =0 else, be the last exit time of the sequence Xk of independent, identically distributed random variables with EX k + <τ, β>0. We will prove sufficient conditions such that the law of the iterated logarithm holds for tβ as β→0. In discussing the relationships to the maximum Z n =max{Xi, i≦n} we give weaker conditions for the law of the iterated logarithm of Z n (n→τ) than the known conditions.

Keywords

Stochastic Process Probability Theory Mathematical Biology Random Sequence Weak Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • J. Hüsler
    • 1
  1. 1.Dept. of Mathematical StatisticsUniversity of BernBernSwitzerland

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