## Electronic Journal of Probability

### Generalised Stable Fleming-Viot Processes as Flickering Random Measures

#### 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.

#### Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 84, 2418-2437.

Dates
Accepted: 3 November 2009
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464819545

Digital Object Identifier
doi:10.1214/EJP.v14-712

Mathematical Reviews number (MathSciNet)
MR2563246

Zentralblatt MATH identifier
1190.60040

Subjects
Primary: 60G57: Random measures
Secondary: 60G17: Sample path properties

Rights

#### Citation

Birkner, Matthias; Blath, Jochen. Generalised Stable Fleming-Viot Processes as Flickering Random Measures. Electron. J. Probab. 14 (2009), paper no. 84, 2418--2437. doi:10.1214/EJP.v14-712. https://projecteuclid.org/euclid.ejp/1464819545

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