Accession Number : AD0605638

Title :   LIMITING BEHAVIOR FOR AGE AND POSITIONDEPENDENT BRANCHING PROCESSES.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Conner,Howard E.

Report Date : JUN 1964

Pagination or Media Count : 1

Abstract : In this paper a model is studied for the population transition probabilities for a branching process composed of particles diffusing in a finite interval. The model is in general non-Markovian assuming the branching transformation probabilities for a particle depend on its age and position. The process is described by the random number N sub t (x) of particles in the interval I at time t that are generated by a single particle initially at the point x in I. By considering N sub t (x) as a regenerative process with respect to the random age and position of the initial particle when it is transformed, a functional equation is developed for the generating function for N sub t (x). This functional equation is the basis for the study of the population probabilities P(N sub t (x) = n), n = 0,1,2, ... , as function of x in I and t in (0, infinity). The principal results develop the behavior of N sub t (x) for large t and the dependence of such behavior on x. A convergence is established in distribution for those processes for which N sub t (x) can increase without bound with positive probability as t approaches infinity. (Author)

Descriptors :   (*MATHEMATICAL MODELS, STOCHASTIC PROCESSES), (*STOCHASTIC PROCESSES, NUCLEAR PARTICLES), NEUTRON AGE, PROBABILITY, FUNCTIONS(MATHEMATICS), EQUATIONS, DIFFUSION

Distribution Statement : APPROVED FOR PUBLIC RELEASE