Limiting diffusions for population-size dependent branching processes
- 1 March 1977
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 14 (1) , 14-24
- https://doi.org/10.2307/3213257
Abstract
A classical theorem on the convergence to a diffusion of a sequence of branching processes will be proved in the case where the branching processes are modified to allow dependence on population size of the generating function governing reproduction. Some recent semigroup convergence theorems due to Kurtz (1969), (1975) provide the main tools.Keywords
This publication has 7 references indexed in Scilit:
- Semigroups of Conditioned Shifts and Approximation of Markov ProcessesThe Annals of Probability, 1975
- Diffusion Approximations of Branching ProcessesThe Annals of Mathematical Statistics, 1971
- Extensions of Trotter's operator semigroup approximation theoremsJournal of Functional Analysis, 1969
- On Feller's branching diffusion processesČasopis pro pěstování matematiky, 1969
- Diffusion processes in one dimensionTransactions of the American Mathematical Society, 1954
- The Parabolic Differential Equations and the Associated Semi-Groups of TransformationsAnnals of Mathematics, 1952
- Diffusion Processes in GeneticsPublished by University of California Press ,1951