论文标题
完全相关的共生分支模型的长期行为
Longtime behavior of completely positively correlated Symbiotic Branching Model
论文作者
论文摘要
我们研究了连续状态共生分支模型（SBM）的长期行为。 SBM可以看作是统一的模型，概括了垫脚石模型，相互催化的分支过程和抛物线代理模型。它是由Etheridge和Fleischmann于2004年推出的。这些模型的关键参数是驾驶Brownian动议之间的本地相关性$ρ$。所有SBM的长期行为都表现出两个人群之间的共存和不保存之间的二分法，具体取决于迁移的复发和瞬态，在许多情况下，也要根据分支率。理解SBM长期行为的最显着差距是瞬态方案中的正相关。在本文中，我们对SBM的长期行为进行了精确描述，并具有$ρ= 1 $，并不一定是相同的初始条件。
We study the longtime behavior of a continuous state Symbiotic Branching Model (SBM). SBM can be seen as a unified model generalizing the Stepping Stone Model, Mutually Catalytic Branching Processes, and the Parabolic Anderson Model. It was introduced by Etheridge and Fleischmann in 2004. The key parameter in these models is the local correlation $ρ$ between the driving Brownian Motions. The longtime behavior of all SBM exhibits a dichotomy between coexistence and non-coexistence of the two populations depending on the recurrence and transience of the migration and also in many cases on the branching rate. The most significant gap in the understanding of the longtime behavior of SBM is for positive correlations in the transient regime. In this article we give a precise description of the longtime behavior of the SBM with $ρ=1$ with not necessarily identical initial conditions.
