Electronic Journal of Probability

Affine processes with compact state space

Paul Krühner and Martin Larsson

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Abstract

The behavior of affine processes, which are ubiquitous in a wide range of applications, depends crucially on the choice of state space. We study the case where the state space is compact, and prove in particular that (i) no diffusion is possible; (ii) jumps are possible and enforce a grid-like structure of the state space; (iii) jump components can feed into drift components, but not vice versa. Using our main structural theorem, we classify all bivariate affine processes with compact state space. Unlike the classical case, the characteristic function of an affine process with compact state space may vanish, even in very simple cases.

Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 29, 23 pp.

Dates
Received: 23 June 2017
Accepted: 12 March 2018
First available in Project Euclid: 30 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1522375269

Digital Object Identifier
doi:10.1214/18-EJP156

Mathematical Reviews number (MathSciNet)
MR3785399

Zentralblatt MATH identifier
1390.60277

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces 60J27: Continuous-time Markov processes on discrete state spaces 60J75: Jump processes

Keywords
affine processes compact state space Markov chains

Rights
Creative Commons Attribution 4.0 International License.

Citation

Krühner, Paul; Larsson, Martin. Affine processes with compact state space. Electron. J. Probab. 23 (2018), paper no. 29, 23 pp. doi:10.1214/18-EJP156. https://projecteuclid.org/euclid.ejp/1522375269


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References

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