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A Williams decomposition for spatially dependent superprocesses

Abstract : We present a genealogy for superprocesses with a non-homogeneous quadratic branching mechanism, relying on a weighted version of the superprocess and a Girsanov theorem. We then decompose this genealogy with respect to the last individual alive (William's 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 diff usion and the superdiffusion are provided.
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https://hal.archives-ouvertes.fr/hal-00601539
Contributor : Olivier Hénard <>
Submitted on : Saturday, June 18, 2011 - 1:50:38 PM
Last modification on : Wednesday, April 15, 2015 - 4:11:05 PM
Long-term archiving on: : Monday, September 19, 2011 - 2:21:14 AM

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Jean-François Delmas, Olivier Hénard. A Williams decomposition for spatially dependent superprocesses. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2013, 18, pp.1-43. ⟨10.1214/EJP.v18-1801⟩. ⟨hal-00601539⟩

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