The Annals of Applied Probability

Polynomial jump-diffusions on the unit simplex

Christa Cuchiero, Martin Larsson, and Sara Svaluto-Ferro

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Abstract

Polynomial jump-diffusions constitute a class of tractable stochastic models with wide applicability in areas such as mathematical finance and population genetics. We provide a full parameterization of polynomial jump-diffusions on the unit simplex under natural structural hypotheses on the jumps. As a stepping stone, we characterize well-posedness of the martingale problem for polynomial operators on general compact state spaces.

Article information

Source
Ann. Appl. Probab., Volume 28, Number 4 (2018), 2451-2500.

Dates
Received: December 2016
Revised: August 2017
First available in Project Euclid: 9 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1533780278

Digital Object Identifier
doi:10.1214/17-AAP1363

Mathematical Reviews number (MathSciNet)
MR3843834

Zentralblatt MATH identifier
06974756

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
Polynomial processes unit simplex stochastic models with jumps Wright–Fisher diffusion stochastic invariance

Citation

Cuchiero, Christa; Larsson, Martin; Svaluto-Ferro, Sara. Polynomial jump-diffusions on the unit simplex. Ann. Appl. Probab. 28 (2018), no. 4, 2451--2500. doi:10.1214/17-AAP1363. https://projecteuclid.org/euclid.aoap/1533780278


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