Electronic Journal of Probability

Probability measure-valued polynomial diffusions

Christa Cuchiero, Martin Larsson, and Sara Svaluto-Ferro

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1553565781

Digital Object Identifier
doi:10.1214/19-EJP290

Mathematical Reviews number (MathSciNet)
MR3933209

Zentralblatt MATH identifier
07055668

Subjects
Primary: 60J68: Superprocesses 60G57: Random measures

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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