Probability measure-valued polynomial diffusions
Martin Larsson and
Papers from arXiv.org
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 by Cuchiero et al. (2012) and Filipovic and Larsson (2016) 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.
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
http://arxiv.org/pdf/1807.03229 Latest version (application/pdf)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1807.03229
Access Statistics for this paper
More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().