Limit Theorems for Stopped Random Walks

  • Allan Gut
Part of the Applied Probability book series (APPLIEDPROB, volume 5)


Classical limit theorems such as the law of large numbers, the central limit theorem and the law of the iterated logarithm are statements concerning sums of independent and identically distributed random variables, and thus, statements concerning random walks. Frequently, however, one considers random walks evaluated after a random number of steps. In sequential analysis, for example, one considers the time points when the random walk leaves some given finite interval. In renewal theory one considers the time points generated by the so called renewal counting process. For random walks on the whole real line one studies the first passage times across horizontal levels, where, in particular, the zero level corresponds to the first ascending ladder epoch. In reliability theory one may, for example, be interested in the total cost for the replacements made during a fixed time interval and so on.


Random Walk Limit Theorem Central Limit Theorem Iterate Logarithm Complete Convergence 
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 Science+Business Media New York 1988

Authors and Affiliations

  • Allan Gut
    • 1
  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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