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The discrete approximation of a class of continuous-state nonlinear branching processes
- Source :
- SCIENTIA SINICA Mathematica. 49:403
- Publication Year :
- 2019
- Publisher :
- Science China Press., Co. Ltd., 2019.
-
Abstract
- In this paper we consider a general continuous-state nonlinear branching process which can be identified as a nonnegative solution to a nonlinear version of the stochastic differential equation driven by Brownian motion and Poisson random measure. Intuitively, this process is a branching process with population-size-dependent branching rates and with competition. We construct a sequence of discrete-state nonlinear branching processes and prove that it converges weakly to the continuous-state nonlinear branching process by using tightness arguments and convergence criteria on infinite-dimensional space.
Details
- ISSN :
- 16747216
- Volume :
- 49
- Database :
- OpenAIRE
- Journal :
- SCIENTIA SINICA Mathematica
- Accession number :
- edsair.doi...........9c27e1a8d613fd3782ec5681b84e3441