A Renewal Theorem for Random Walks with Time Stationary Random Distribution Function

  • Hong, Dug-Hun (School of Mechanical and Automotive Engineering, Catholic University of Taegu Hyosung, Kyungbuk, 712-702)
  • Published : 1996.03.01

Abstract

Sums of independent random variables $S_n = X_1 + X_ + cdots + X_n$ are considered, where the X$_{n}$ are chosen according to a stationary process of distributions. Given the time t .geq. O, let N (t) be the number of indices n for which O < $S_n$ $\geq$ t. In this set up we prove that N (t)/t converges almost surely and in $L^1$ as t longrightarrow $\infty$, which generalizes classical renewal theorem.m.

Keywords

References

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