Hostname: page-component-7dd5485656-s6l46 Total loading time: 0 Render date: 2025-10-31T00:56:36.979Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on random walks at constant speed

Published online by Cambridge University Press:  01 July 2016

M. S. Bartlett
M. S. Bartlett*
Affiliation:
Address: 117 Littlehampton Road, Worthing BN13 1QU, Sussex, England.
Get access Rights & Permissions [Opens in a new window]

Extract

While the general principles involved in the formulation of random walk and Brownian motion equations (whether the random changes are directly on the position of a particle or individual, or on the velocity) are well-known, there are various situations considered in the literature involving the assumption of a constant speed (in magnitude). Thus the derivation by Goldstein (1951) of a one-dimensional wave-like equation involved the tacit assumption Ut = ± a, where Ut is the vector velocity dRt /dt,Rt being the (column) position vector (Bartlett (1957)). Biological models may involve the assumption of individuals moving at constant speed (cf. Kendall (1974)). Finally, the derivation of Schrodinger-type equations from Brownian motion models has sometimes involved the assumption U′t Ut = c 2, where c is the velocity of light (Cane (1967), (1975)).

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 4 , December 1978 , pp. 704 - 707
Copyright
Copyright © Applied Probability Trust 1978 

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.)

Article purchase

Temporarily unavailable

References

Bartlett, M. S. (1957) Some problems associated with random velocity. Publ. Inst. Statist. Univ. Paris 6, 261–270.Google Scholar
Bartlett, M. S. (1975) The paradox of probability in physics. In Probability, Statistics. and Time. Chapman and Hall, London.Google Scholar
Cane, V. R. (1967) Random walks and physical processes. Bull. Internat. Statist. Inst. 42(1), 622–640.Google Scholar
Cane, V. R. (1975) Diffusion models with relativity effects. In Perspectives in Probability and Statistics, ed. Gani, J., distributed by Academic Press, London for the Applied Probability Trust, Sheffield, 263–273.Google Scholar
Goldstein, S. (1951) On diffusion by discontinuous movements, and on the telegraph equation. Quart. J. Mech. Appl. Math. 4, 129–156.Google Scholar
Kendall, D. G. (1974) Pole-seeking Brownian motion and bird navigation. J.R. Statist. Soc. B 36, 365–417.Google Scholar