论文标题
与移民的计算资源相关分支过程的计算可能平衡的数值方面
Numerical Aspects of Computing Possible Equilibria for Resource Dependent Branching Processes with Immigration
论文作者
论文摘要
本文研究了在所谓的资源依赖分支过程中产生的平衡方程解决方案的稳定性。我们认为，这些新模型建立在Bruss（1984 A）已经提出的模型上，在Bruss and Duerinckx（2015）中进行了精制和详细说明，现在扩展到允许移民，适合应对人类人群的特定特性。我们的主要兴趣是在这里了解移民可能导致平衡的条件。同时，我们想将依赖资源的分支过程宣传为研究此类问题的最佳模型。 对于几个重要的稳定性问题，我们获得的新模型的平衡方程都是清晰且内容丰富的。我们提供的特定示例的研究的目的是查看移民的影响最明显的地方，并且在整合的努力增加的程度可以应对不稳定的危险。此外，我们讨论了模型的优点和较弱的点，还简要介绍了连续状态，连续的分支过程作为替代方案。
This article studies the stability of solutions of equilibrium equations arising in so-called resource dependent branching processes. We argue that these new models, building on the model already presented by Bruss (1984 a), refined and elaborated in Bruss and Duerinckx (2015) and now extended to allow immigration, are suitable to cope with specific properties of human populations. Our main interest is here to understand under which conditions immigration may lead to an equilibrium. At the same time, we would like to advertize resource dependent branching processes as possibly the best models to study such questions. The equilibrium equations for the new models we obtain are clear and informative for several important stability questions. The goal of the study of the specific examples we provide is to see where the impact of immigration is most visible, and in how far increased efforts of integration can cope with dangers of instability. Moreover we discuss the advantages and a weaker point of our model, and also include a brief look at continuous-state, continuous-time branching processes as an alternative.
