Electronic Journal of Probability

Probability measure-valued polynomial diffusions

Christa Cuchiero, Martin Larsson, and Sara Svaluto-Ferro

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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.

Article information

Electron. J. Probab., Volume 24 (2019), paper no. 30, 32 pp.

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

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Zentralblatt MATH identifier

Primary: 60J68: Superprocesses 60G57: Random measures

probability measure-valued processes polynomial processes Fleming–Viot type processes interacting particle systems martingale problem maximum principle dual process

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Cuchiero, Christa; Larsson, Martin; Svaluto-Ferro, Sara. Probability measure-valued polynomial diffusions. Electron. J. Probab. 24 (2019), paper no. 30, 32 pp. doi:10.1214/19-EJP290. https://projecteuclid.org/euclid.ejp/1553565781

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