ON THE THEORY OF AGE-DEPENDENT STOCHASTIC BRANCHING PROCESSES
RAND CORP SANTA MONICA CA
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The following problem which is of possible biological, chemical and physical interest is investigated. A particle existing at time t sub 1 0 is assumed to have probabilities q sub n or 0, of being transformed into n similar particles at some random time t 0. Assume that a start is made with a single particle at t 0. Under the hypothesis that any particle has a life- length probability distribution independent of its time of birth and of the number of other particles existing at this time, the problem is to determine the probability distribution of Zt, the number of particles in existence at time t. The problem is restricted as far as detailed exposition goes, to the special case where only binary transformations occur that is, one particle can be transformed only into two others. This is the most important case biologically, and the methods employed to deal with this case are easily extended to deal with the general case with n-ary transformations.
- Statistics and Probability