论文标题
Yaglom型限制了带有布朗运动的分支运动定理
Yaglom-type limit theorems for branching Brownian motion with absorption
论文作者
论文摘要
我们考虑了一维分支布朗运动，其中颗粒在原点被吸收。我们假设，当粒子分支时，后代分布是超临界的，但是粒子被朝向原点的临界漂移，以使过程最终随概率一个而灭绝。我们建立了精确的渐近学，因为该过程在很长一段时间内生存的概率是基于Kesten（1978）和Berestycki，Berestycki和Schweinsberg（2014）的先前结果。我们还证明了Yaglom型的限制定理，该过程的行为旨在生存长时间，为Kesten（1978）首先解决的问题提供了基本完整的答案。这些结果证明的一个重要工具是可以观察到连续的状态分支过程的某些一定的收敛性。我们的证明结合了可能在其他分支模型中使用的新想法。
We consider one-dimensional branching Brownian motion in which particles are absorbed at the origin. We assume that when a particle branches, the offspring distribution is supercritical, but the particles are given a critical drift towards the origin so that the process eventually goes extinct with probability one. We establish precise asymptotics for the probability that the process survives for a large time t, building on previous results by Kesten (1978) and Berestycki, Berestycki, and Schweinsberg (2014). We also prove a Yaglom-type limit theorem for the behavior of the process conditioned to survive for an unusually long time, providing an essentially complete answer to a question first addressed by Kesten (1978). An important tool in the proofs of these results is the convergence of a certain observable to a continuous state branching process. Our proofs incorporate new ideas which might be of use in other branching models.
