论文标题
关于简单可交换的片段钙化过程中片段数量的爆炸
On the explosion of the number of fragments in the simple exchangeable fragmentation-coalescence processes
论文作者
论文摘要
我们考虑可交换的片段凝集（EFC）过程，其中凝结是多重而不是同时的，如$λ$ - 浓度，并且片段以有限的速率脱离了单个块进入无限大小的亚块。发现了足够的条件，可以爆炸（即达到$ \ infty $），而无限元则是出口边界或入口边界。在定期改变碎片和凝结机制的情况下，我们发现边界$ \ indty $可以是出口，入口或常规边界的机制。在后一种常规情况下，EFC过程瞬间离开了无数块数量的分区集，并立即返回。证明是基于一个新的充分爆炸条件，用于积极的连续时间马尔可夫链，这是独立的。
We consider the exchangeable fragmentation-coagulation (EFC) processes, where the coagulations are multiple and not simultaneous, as in a $Λ$-coalescent, and the fragmentations dislocate at finite rate an individual block into sub-blocks of infinite size. Sufficient conditions are found for the block-counting process to explode (i.e. to reach $\infty$) or not and for infinity to be an exit boundary or an entrance boundary. In a case of regularly varying fragmentation and coagulation mechanisms, we find regimes where the boundary $\infty$ can be either an exit, an entrance or a regular boundary. In the latter regular case, the EFC process leaves instantaneously the set of partitions with an infinite number of blocks and returns to it immediately. Proofs are based on a new sufficient condition of explosion for positive continuous-time Markov chains, which is of independent interest.
