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A stochastic population process and its application to bubble chamber measurements

Published online by Cambridge University Press:  14 July 2016

P. J. Brockwell  and
J. E. Moyal
P. J. Brockwell
Affiliation:
Argonne National Laboratory
J. E. Moyal
Affiliation:
Argonne National Laboratory
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Extract

A particle travels along the half-line [0,∞) in such a way that it has probability λδu + o(δu) of generating an event in any small element (u,u + δu) of its track. The particle is observed only in the line segment 0 ≦ u ≦ x and successive events occur at X1, X2, …, Xn (0 ≦ X1 ≦ X2 ≦ … ≦ Xn ≦ x) where X1, …,Xn are random variables and the number n of events in [0, x] is also random. The distances constitute a finite univariate population process as defined by Moyal [1], the individuals being the distances Yi with state space [0, x].

Type
Short Communications
Information
Journal of Applied Probability , Volume 3 , Issue 1 , June 1966 , pp. 280 - 284
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Moyal, J. E. (1962) The general theory of stochastic population processes. 108, 1–31.Google Scholar