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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

Darroch, J. N. (1966) Identities for passage times with applications to recurrent events and homogeneous differential equations. J. Appl. Prob. 3, 435–444.CrossRefGoogle Scholar
Feller, W. (1968) An Introduction to Probability Theory and its Applications. Vol. 1, 3rd Edition. Wiley International Edition.Google Scholar
Freedman, D. A. (1962) An arc-sine law for Markov chains. Proc. Amer. Math. Soc. 14, 680–684.Google Scholar
Heyde, C. C. (1969) On extremal factorization and recurrent events. J. R. Statist. Soc. B31, 72–79.Google Scholar
Seth, A. (1963) The correlated unrestricted random walk. J. R. Statist. Soc. B25, 394–400.Google Scholar