Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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On a Stopping Rule for the Random Walks with Time Stationary Random Distribution Function

  • Hong, Dug-Hun (Department of Statistics, Catholic University of Taegu-Hyosung, Kyungbuk 713-702) ;
  • Oh, Kwang-Sik (Department of Statistics, Catholic University of Taegu-Hyosung, Kyungbuk 713-702) ;
  • Park, Hee-Joo (Department of Computer, Kyungpook Sanup University, Taegu 701-702)
  • Published : 1995.12.01
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Abstract

Sums of independent random variables $S_n = X_1 + \cdots + X_n$ are considered, where the $X_n$ are chosen according to a stationary process of distributions. For $c > 0$, let $t_c$ be the smallest positive integer n such that $$\mid$S_n$\mid$ > cn^{\frac{1}{2}}$. In this set up we are concerned with finiteness of expectation of $t_c$ and we have some results of sign-invariant process as applications.

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References

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