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.
| Translated title of the contribution | The discrete approximation of a class of continuous-state nonlinear branching processes |
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| Original language | Chinese (Traditional) |
| Pages (from-to) | 403-414 |
| Number of pages | 12 |
| Journal | Scientia Sinica Mathematica |
| Volume | 49 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2019 |