Asymptotic fluctuations of supercritical general branching processes

超临界一般支化过程的渐近涨落

• 批准号: 460482685
• 负责人: Professor Dr. Matthias Meiners
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/460482685?language=en
• 关键词: Asymptotic; fluctuations; supercritical; general; branching

We study supercritical single- and multi-type general (Crump-Mode-Jagers) branching processes. The goal is to precisely understand their asymptotic bevahiour in time beyond the law of large numbers. The difficulty comes from the fact that in certain cases, periodic fluctuations between the scales of the law of large numbers and the central limit theorem arise. These periodicities are intimately connected with convergence of complex martingales and complex smoothing equations. Methods come from the fields of branching processes, convergence of stochastic processes, martingale theory, renewal and Markov renewal theory, Laplace transformation, and the theory of complex smoothing equations.

我们研究超临界单和多类型的一般（Crump-Mode-Jagers）分支过程。我们的目标是精确地理解它们在时间上超越大数定律的渐近性质。困难来自于这样一个事实，即在某些情况下，大数定律和中心极限定理的尺度之间会出现周期性波动。这些周期性与复鞅和复光滑方程的收敛性密切相关。方法来自分支过程，随机过程的收敛，鞅理论，更新和马尔可夫更新理论，拉普拉斯变换和复光滑方程理论等领域。