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August, 1976 Oscillations of Continuous Symmetric Random Walk
J. P. Imhof
Ann. Probab. 4(4): 662-666 (August, 1976). DOI: 10.1214/aop/1176996035


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.


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J. P. Imhof. "Oscillations of Continuous Symmetric Random Walk." Ann. Probab. 4 (4) 662 - 666, August, 1976.


Published: August, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0339.60051
MathSciNet: MR410935
Digital Object Identifier: 10.1214/aop/1176996035

Primary: 60G50
Secondary: 60C05

Keywords: fluctuation theory , Oscillations , Random walk

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 4 • August, 1976
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