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A semi-infinite random walk with discrete steps

Published online by Cambridge University Press:  24 October 2008

L. R. Shenton
L. R. Shenton
Affiliation:
College of Technology Manchester I
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1. A particle executes a random walk over the possible positions x = 0,1,2,…, its initial position being x = d ≥ 0. At the nth step it occupies the position x with probability pn (x | d)and is in the state (n, x). The transition from (n, x) to (n + 1, y) has the probability px, v given by

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 3 , July 1955 , pp. 442 - 448
Copyright
Copyright © Cambridge Philosophical Society 1955

References

REFERENCES

(1)Feller, W.An introduction to probability theory and its applications, vol. 1 (New York, 1950).Google Scholar
(2)Kac, Mark. Random walk and the theory of Brownian motion. Amer. math. Mon. 54 (1947), 369–91.CrossRefGoogle Scholar
(3)Lauwerier, H. A.A linear random walk with a barrier. Appl. sci. Res., Hague, B, 2 (1951), 294–300.CrossRefGoogle Scholar
(4)Szegö, G.Orthogonal polynomials (Colloq. Publ. Amer. math. Soc. 1939).Google Scholar
(5)Uspensky, J. V.Introduction to mathematical probability (New York, 1937).Google Scholar