Open Access
2018 Affine processes with compact state space
Paul Krühner, Martin Larsson
Electron. J. Probab. 23: 1-23 (2018). DOI: 10.1214/18-EJP156


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.


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Paul Krühner. Martin Larsson. "Affine processes with compact state space." Electron. J. Probab. 23 1 - 23, 2018.


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

zbMATH: 1390.60277
MathSciNet: MR3785399
Digital Object Identifier: 10.1214/18-EJP156

Primary: 60J25 , 60J27 , 60J75

Keywords: Affine processes , compact state space , Markov chains

Vol.23 • 2018
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