论文标题
两个连续状态分支过程之间的相对频率与移民及其家谱
The relative frequency between two continuous-state branching processes with immigration and their genealogy
论文作者
论文摘要
当存在两个（可能不同的分布）连续分支过程中具有移民的连续分支过程时，我们研究其中一个的相对频率在一组密集的时间被迫恒定时。这导致了SDE，其独特的强解决方案将是$λ$ - 空气对称频率过程（$λ$ -AFP）的定义。我们证明这是一个陷入困境的过程，当总质量倾向于无穷大时，我们计算出较大的人口限制。这使我们能够研究该过程围绕其确定性极限的波动。此外，我们发现$λ$ -AFP的条件具有偶数偶。双重可以用选择，（配位）突变，成对分支（效率），合并和新的组成部分来解释双重二元组合，这些成分来自繁殖机制之间的不对称性。在一对均等的连续分支过程的特定情况下，相关的$λ$ -AFP将是$λ$ -Coalescent的双重。将每个连续状态分支过程发送到其关联的$λ$ - 涂层（根据前一个过程）的地图是度量空间之间的同态性。
When two (possibly different in distribution) continuous-state branching processes with immigration are present, we study the relative frequency of one of them when the total mass is forced to be constant at a dense set of times. This leads to a SDE whose unique strong solution will be the definition of a $Λ$-asymmetric frequency process ($Λ$-AFP). We prove that it is a Feller process and we calculate a large population limit when the total mass tends to infinity. This allows us to study the fluctuations of the process around its deterministic limit. Furthermore, we find conditions for the $Λ$-AFP to have a moment dual. The dual can be interpreted in terms of selection, (coordinated) mutation, pairwise branching (efficiency), coalescence, and a novel component that comes from the asymmetry between the reproduction mechanisms. In the particular case of a pair of equally distributed continuous-state branching processes, the associated $Λ$-AFP will be the dual of a $Λ$-coalescent. The map that sends each continuous-state branching process to its associated $Λ$-coalescent (according to the former procedure) is a homeomorphism between metric spaces.
