It is well understood that a supercritical superprocess is equal in law to a discrete Markov branching process whose genealogy is dressed in a Poissonian way with immigration which initiates subcritical superprocesses. The Markov branching process corresponds to the genealogical description of prolific individuals, that is, individuals who produce eternal genealogical lines of descent, and is often referred to as the skeleton or backbone of the original superprocess. The Poissonian dressing along the skeleton may be considered to be the remaining non-prolific genealogical mass in the superprocess. Such skeletal decompositions are equally well understood for continuous-state branching processes (CSBP).In a previous article [16] we developed an SDE approach to study the skeletal representation of CSBPs, which provided a common framework for the skeletal decompositions of supercritical and (sub)critical CSBPs. It also helped us to understand how the skeleton thins down onto one infinite line of descent when conditioning on survival until larger and larger times, and eventually forever.Here our main motivation is to show the robustness of the SDE approach by expanding it to the spatial setting of superprocesses. The current article only considers supercritical superprocesses, leaving the subcritical case open.

中文翻译：

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超过程的骨架随机微分方程

众所周知，超临界超过程在法律上等同于离散马尔可夫分支过程，其谱系以泊松方式穿着，移民启动亚临界超过程。马尔可夫分支过程对应于家谱描述多产的个体，即产生永恒家谱血统的个体，通常被称为骨骼要么骨干原始的超级进程。沿着骨骼的泊松敷料可以被认为是超级过程中剩余的非多产系谱质量。对于连续状态分支过程 (CSBP)，这种骨架分解同样得到很好的理解。在之前的文章 [16] 中，我们开发了一种 SDE 方法来研究 CSBP 的骨架表示，它为超临界和 (CSBP) 的骨架分解提供了一个通用框架。次）临界 CSBP。它还帮助我们理解当以生存为条件直到越来越长的时间，并最终永远存在时，骨架如何变薄到一条无限的下降线。这里我们的主要动机是通过将 SDE 方法扩展到空间来展示它的鲁棒性超级进程的设置。目前的文章只考虑超临界超过程，