Open Access
2019 Probability measure-valued polynomial diffusions
Christa Cuchiero, Martin Larsson, Sara Svaluto-Ferro
Electron. J. Probab. 24: 1-32 (2019). DOI: 10.1214/19-EJP290


We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming–Viot process is a particular example. The defining property of finite dimensional polynomial processes considered in [8, 21] is transferred to this infinite dimensional setting. This leads to a representation of conditional marginal moments via a finite dimensional linear PDE, whose spatial dimension corresponds to the degree of the moment. As a result, the tractability of finite dimensional polynomial processes are preserved in this setting. We also obtain a representation of the corresponding extended generators, and prove well-posedness of the associated martingale problems. In particular, uniqueness is obtained from the duality relationship with the PDEs mentioned above.


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Christa Cuchiero. Martin Larsson. Sara Svaluto-Ferro. "Probability measure-valued polynomial diffusions." Electron. J. Probab. 24 1 - 32, 2019.


Received: 17 August 2018; Accepted: 2 March 2019; Published: 2019
First available in Project Euclid: 26 March 2019

zbMATH: 07055668
MathSciNet: MR3933209
Digital Object Identifier: 10.1214/19-EJP290

Primary: 60G57 , 60J68

Keywords: Dual process , Fleming–Viot type processes , interacting particle systems , Martingale problem , maximum principle , Polynomial processes , probability measure-valued processes

Vol.24 • 2019
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