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A note on random walks

Published online by Cambridge University Press:  14 July 2016

R. M. Phatarfod ,
T. P. Speed  and
A. M. Walker
R. M. Phatarfod*
Affiliation:
University of Essex
T. P. Speed
Affiliation:
University of Sheffield
A. M. Walker
Affiliation:
University of Sheffield
*
*On leave from Monash University.
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Extract

Let {Xn} be a random walk between reflecting barriers at 0 and a > 0 with jumps {Zn}. By we mean the random walk between absorbing barriers at — a and 0+ with the same jumps {Zn}. It has been known for some time that when {Zn} is a sequence of mutually independent and identically distributed random variables, and 0 ≦x <a, we have for all n:

Type
Short Communications
Information
Journal of Applied Probability , Volume 8 , Issue 1 , March 1971 , pp. 198 - 201
Copyright
Copyright © Applied Probability Trust 1971 

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References

[1] Birkhoff, G. (1967) Lattice Theory. (3rd Edition) Amer. Math. Soc. Google Scholar
[2] Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, London.Google Scholar
[3] Feller, W. (1968) Introduction to Probability Theory and its Applications. (3rd Edition) Wiley, New York.Google Scholar
[4] Finch, P. D. (1960–61) Storage problems along a production line of continuous flow. Ann. Univ. de Eotvos. Sect. Math. III, 67–84.Google Scholar
[5] Ghosal, A. (1964) Some results in the theory of inventory. Biometrika 51, 487–490.Google Scholar
[6] Lindley, D. V. (1959) Contribution to the discussion on the paper “Geometric distributions in the theory of queues” by C. B. Winsten. J. R. Statist. Soc. B 21, 1–22.Google Scholar
[7] Lindley, D. V. (1952) The theory of queues with a single server. Proc. Camb. Phil. Soc. 48, 177–189.Google Scholar
[8] Loynes, R. M. (1965) On a property of the random walks describing simple queues and dams. J. R. Statist. Soc. B 27, 125–129.Google Scholar
[9] Prabhu, N. U. (1962) Elementary methods for some waiting time problems. Operat. Res. 10, 559–566.Google Scholar