项目名称: 关于几类新型两性分枝过程及其相关问题研究
项目编号: No.11301133
项目类型: 青年科学基金项目
立项/批准年度: 2014
项目学科: 数理科学和化学
项目作者: 马世霞
作者单位: 河北工业大学
项目金额: 22万元
中文摘要: 分枝过程不仅在随机过程理论领域占有重要的地位,而且在种群繁衍,基因遗传,流行病传播等领域有广泛应用。该项目以几类新型的两性分枝过程为研究对象,包括Markov环境中的两性分枝过程,平稳遍历环境中的两性分枝过程,连续时间年龄相依的两性分枝过程,以及带移民的两性分枝过程模型。除了它们的灭绝概率问题,我们还将研究以上单个两性分枝过程的渐近收敛,以及分枝过程列弱收敛到反射随机过程等问题。在我们已有研究工作的基础上,采取的主要研究方法是随机比较,更新理论和泛函极限理论等。该项目旨在理论上进一步发展两性分枝过程理论,为应用领域提供新的模型和研究结果。
中文关键词: 分枝过程;两性分枝过程;随机环境;灭绝概率;风险控制
英文摘要: The study of branching processes has very important significance in stochastic process theory, and branching processes have extensive application in population propagation、gene inheritance、 epidemic diffusion and so on. In this item, we investigate some new classes of bisexual branching processes models, including bisexual branching processes in Markov environments, bisexual branching processess in stationary ergodic environments, the continuous time age-dependent bisexual branching processes, bisexual branching process model with immigration. Except for the extinction probability problem, we also investigate their asymptotic convergence and the convergence in distribution to reflected stochastic processes. On the basis of our research work, we mainly apply stochastic compare, renewal theory and functional limit theory etc. The purpose of this item is to develop the theory of bisexual branching processes, and supply some new models and research result for practical application fields.
英文关键词: Branching process;Bisexual branching process;Random environment;Extinction probability;Risk control