论文标题
大型初始状态的连续时间离散状态空间分支过程的渐近学
Asymptotics of continuous-time discrete state space branching processes for large initial state
论文作者
论文摘要
由于初始状态倾向于无穷大，因此提供了具有离散状态空间的连续时间分支过程的缩放限制。根据后代分布的平均值和/或方差的有限或非限制性，限制在一般时间内均匀的高斯过程中，时间均匀固定的普遍性Ornstein-Uhlenbeck类型过程或连续状态分支过程。我们还提供了转移结果，显示了后代分布的概率生成函数的特定渐近关系如何将分支过程的一维分布的概率产生。
Scaling limits for continuous-time branching processes with discrete state space are provided as the initial state tends to infinity. Depending on the finiteness or non-finiteness of the mean and/or the variance of the offspring distribution, the limits are in general time-inhomogeneous Gaussian processes, time-inhomogeneous generalized Ornstein-Uhlenbeck type processes or continuous-state branching processes. We also provide transfer results showing how specific asymptotic relations for the probability generating function of the offspring distribution carry over to those of the one-dimensional distributions of the branching process.
