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Exact fluctuation results for Markov-dependent coin-tossing

Published online by Cambridge University Press:  14 July 2016

J. N. Darroch  and
Heather J. Whitford
J. N. Darroch
Affiliation:
Flinders University of South Australia
Heather J. Whitford
Affiliation:
Flinders University of South Australia
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Abstract

Feller (1968) showed that the probability functions of each of three random variables associated with coin-tossing (independent, simple, symmetric random walk) are (a) the same (except at the end points), (b) approximately arc-sine. In this paper these two properties are shown to hold for Markov-dependent coin-tossing (Markov-dependent, simple, symmetric random walk).

Keywords

ARC-SINEMARKOV DEPENDENTRANDOM WALKFIRST MAXIMUMLAST RETURNCOIN TOSSING
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 158 - 168
Copyright
Copyright © Applied Probability Trust 1972 

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References

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