Zähle, Henryk2009-01-142009-01-142009-01-14http://hdl.handle.net/2003/2599810.17877/DE290R-14437A certain class of stochastic differential equations, containing the Cox-Ingersoll-Ross model and the geometric Brownian motion, is considered. The corresponding solutions are approximated weakly by discrete-time population-size-dependent Galton-Watson processes with immigration. The long-time behavior of the limiting processes is also investigated.enPreprints der Fakultät für Mathematik;2009-01stochastic differential equationGalton-Watson processpopulationsize-dependent branchingweak convergencemartingale problemDoob-Meyer decompositionCox-Ingersoll-Ross model610preprint