Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-09T03:47:36.082Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

Extract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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