Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-21T22:56:02.888Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffusion with “collisions” between particles

Published online by Cambridge University Press:  14 July 2016

T. E. Harris
T. E. Harris*
Affiliation:
The Rand Corporation (University of Southern California from February 1966)
Get access Rights & Permissions [Opens in a new window]

Extract

First consider two particles diffusing on the same line, with positions at time t given by y1(t) and y2(t) respectively. We suppose that they cannot pass one another, so that if initially y1(0) < y2(0), then . As long as the two particles are not in contact, we suppose that each moves, independently of the other, according to the Wiener process. We must also prescribe what happens when collisions occur. There seems to be no unique natural way to do this, and we shall adopt a method recommended by its mathematical convenience. However, we shall see that there are two possible motivations for the prescription, one in terms of random walks, the other in terms of a more mechanical model.

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 2 , December 1965 , pp. 323 - 338
Copyright
Copyright © Applied Probability Trust 

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

[1] Doob, J. L. (1942) The Brownian movement and stochastic equations. Ann. Math. 43, 351–369.Google Scholar
[2] Doob, J. L. (1949) Time series and harmonic analysis. Proc. First Berkeley Symposium on Mathematical Statistics and Probability, U. of California Press.Google Scholar
[3] Doob, J. L. (1953) Stochastic Processes. John Wiley, New York.Google Scholar
[4] Harris, T. E. (1963) The Theory of Branching Processes. Springer and Prentice-Hall.Google Scholar
[5] LЀvy, P. (1948) Processus Stochastiques et Mouvement Brownien. Paris.Google Scholar