Generalised stable Fleming-Viot processes as flickering random measures
Matthias Birkner, University Mainz
Jochen Blath, Technical University Berlin
Abstract
We study some remarkable path-properties of generalised stable
Fleming-Viot processes (including the so-called spatial Neveu
superprocess), inspired by the notion of a ``wandering random
measure'' due to Dawson and Hochberg (1982). In particular, we make
use of Donnelly and Kurtz' (1999) modified lookdown construction to
analyse their longterm scaling properties, exhibiting a rare natural
example of a scaling family of probability laws converging in
f.d.d. sense, but not weakly w.r.t. any of Skorohod's topologies on
path space. This phenomenon can be explicitly described and
intuitively understood in terms of ``sparks'', leading to the
concept of a ``flickering random measure''.
In particular, this completes results of Fleischmann and Wachtel
(2006) about the spatial Neveu process and complements results of
Dawson and Hochberg (1982) about the classical Fleming Viot process.
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