A stochastic population process and its application to bubble chamber measurements

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Abstract
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].

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