Tagged particle processes and their non-explosion criteria

Explosion of continuous-state branching processes with competition in Lévy environment

Using the Lyapunov criteria arguments, we find sufficient conditions on explosion/nonexplosion for continuous-state branching processes with competition in Lévy random environment. In particular, we identify the necessary and sufficient conditions on explosion/nonexplosion when the competition function is a power function and the Lévy measure of the associated branching mechanism is stable.

生灭连续时间随机游走的爆炸与内爆

Explosion and implosion of birth-and-death continuous-time random walks

本文针对非马尔可夫生灭连续时间随机游走，推导其爆炸、内爆的充要正则性判据，并给出两类半马尔可夫情形下的显式判定条件。

灭绝、爆炸与收缩对于具有跳跃的时变随机微分方程

Extinction, explosion and contraction for time-inhomogeneous SDEs with jumps

本文研究了具有跳跃的时变随机微分方程解的灭绝、爆炸与收缩性，并推广了现有文献中的相关结果。

Doubly stochastic Yule cascades (Part II): The explosion problem in the non-reversible case

We analyze the explosion problem for a class of stochastic models introduced in Part I (arXiv:2103.06912), referred to as doubly stochastic Yule cascades. These models arise naturally in the construction of solutions to evolutionary PDEs as well as in purely probabilistic first passage percolation phenomena having a Markov-type statistical dependence, new for this context. Using cut-set arguments and a greedy algorithm, we respectively establish criteria for non-explosion and explosion without requiring the time-reversibility of the underlying branching Markov chain (a condition required in Pa…

广义抛物域中的反射布朗运动：爆炸与超扩散性

Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity

该研究针对广义抛物域中带斜反射的多维无漂移扩散过程，给出爆炸或超扩散瞬态的判定条件，提出并应用了具有独立研究价值的半鞅准则。

关于 CMJ 分支过程爆炸的一个充分条件及其在递归树中的应用

On a sufficient condition for explosion in CMJ branching processes and applications to recursive trees

本文通过有限时间内产生无限路径提供了 CMJ 分支过程爆炸的充分条件，并应用于带适应度的递归树模型，揭示了无限树中节点度数从无限到局部有限的相变现象。