A Williams decomposition for spatially dependent superprocesses
A Williams decomposition for spatially dependent superprocesses
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DOI：
10.1214/ejp.v18-1801
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发表时间：
2011-06
影响因子：
1.4
通讯作者：
Jean-François Delmas;Olivier H'enard
中科院分区：
文献类型：
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作者：
Jean-François Delmas;Olivier H'enard
我们基于 Englander 和 Pinsky 引入的超级过程的加权版本以及吉尔萨诺夫定理，提出了具有非齐次二次分支机制的超级过程的谱系。然后，我们根据最后一个活着的个体来分解这个谱系（威廉姆斯分解）。令灭绝时间趋于无穷大，从根部看超级进程得到Q进程，从顶部看定义另一个进程。提供了包括多型 Feller 扩散（由 Champagnat 和 Roelly 研究）和超扩散的示例。
We present a genealogy for superprocesses with a non-homogeneous quadratic branching mechanism, relying on a weighted version of the superprocess introduced by Englander and Pinsky and a Girsanov theorem. We then decompose this genealogy with respect to the last individual alive (Williams' decomposition). Letting the extinction time tend to infinity, we get the Q-process by looking at the superprocess from the root, and define another process by looking from the top. Examples including the multitype Feller diffusion (investigated by Champagnat and Roelly) and the superdiffusion are provided.