Oscillations of Continuous Symmetric Random Walk

J. P. Imhof

doi:10.1214/aop/1176996035

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Home > Journals > Ann. Probab. > Volume 4 > Issue 4 > Article

August, 1976 Oscillations of Continuous Symmetric Random Walk

J. P. Imhof

Ann. Probab. 4(4): 662-666 (August, 1976). DOI: 10.1214/aop/1176996035

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Abstract

Oscillations are defined for $n$ steps of the random walk formed by partial sums of variables with continuous cdf. When the summands are independent, identically and symmetrically distributed, several distribution free results are obtained relative to the number of oscillations and their lengths. Analogy with the behavior of records in a random sequence is used to obtain limit laws.