随机环境中分支过程拟平稳分布的吸引域

中文摘要 AI 辅助

我们获得了布朗随机环境中次临界稳定连续状态分支过程的拟平稳分布的完整刻画，以及每个成员的吸引域。这些分布构成一个单参数族，其修正的拉普拉斯变换由Tricomi合流超几何函数显式给出。对于每个初始分布，我们确定其条件分布是否收敛到一个拟平稳分布，并在收敛时识别该拟平稳分布。必要且充分的条件以初始分布的尾概率和矩的形式表述。

英文摘要

We obtain a complete characterization of the quasi-stationary distributions of subcritical stable continuous-state branching processes in Brownian random environments, together with the domain of attraction of each member. These distributions form a one-parameter family whose modified Laplace transforms are given explicitly in terms of Tricomi's confluent hypergeometric function. For every initial distribution, we determine whether the conditional law converges to a QSD and identify that QSD whenever it does. The necessary and sufficient criteria are formulated in terms of the tail probabilities and moments of the initial law.

发表机构

• School of Mathematics and Statistics, Beijing Institute of Technology（北京理工大学数学与统计学院）

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