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Stationarity and Ergodicity for an Affine Two-Factor Model

Part of: Markov processes Ergodic theory

Published online by Cambridge University Press:  22 February 2016

Mátyás Barczy ,
Leif Döring ,
Zenghu Li  and
Gyula Pap
Mátyás Barczy*
Affiliation:
University of Debrecen
Leif Döring*
Affiliation:
Universität Zürich
Zenghu Li*
Affiliation:
Beijing Normal University
Gyula Pap*
Affiliation:
University of Szeged
*
∗ Postal address: Faculty of Informatics, University of Debrecen, Pf. 12, H-4010 Debrecen, Hungary. Email address: [email protected]
∗∗ Postal address: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland.
∗∗∗ Postal address: School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China.
∗∗∗∗ Postal address: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary.
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Abstract

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We study the existence of a unique stationary distribution and ergodicity for a two-dimensional affine process. Its first coordinate process is supposed to be a so-called α-root process with α ∈ (1, 2]. We prove the existence of a unique stationary distribution for the affine process in the α ∈ (1, 2] case; furthermore, we show ergodicity in the α = 2 case.

Keywords

Affine processstationary distributionergodicityFoster-Lyapunov criteria

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 37A25: Ergodicity, mixing, rates of mixing
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 3 , September 2014 , pp. 878 - 898
Copyright
© Applied Probability Trust 

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