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On the Exponential Ergodicity of (2+2)-Affine Processes in Total Variation Distances

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  • Shukai Chen

    (Fujian Normal University)

Abstract

We prove an estimate for the variations of transition probabilities of the (2+2)-affine process. From this estimate we deduce the exponential ergodic properties in the total variation distance of the process. The key strategy is the approach of a coupling of the affine process and a coupling of two-type CBI-processes established by stochastic equations.

Suggested Citation

  • Shukai Chen, 2023. "On the Exponential Ergodicity of (2+2)-Affine Processes in Total Variation Distances," Journal of Theoretical Probability, Springer, vol. 36(1), pages 315-330, March.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:1:d:10.1007_s10959-022-01173-1
    DOI: 10.1007/s10959-022-01173-1
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    References listed on IDEAS

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    1. Ma, Chunhua, 2009. "A limit theorem of two-type Galton-Watson branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1710-1716, August.
    2. Xiaowei Zhang & Peter W. Glynn, 2018. "Affine Jump-Diffusions: Stochastic Stability and Limit Theorems," Papers 1811.00122, arXiv.org.
    3. Kyprianou, Andreas E. & Palau, Sandra, 2018. "Extinction properties of multi-type continuous-state branching processes," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3466-3489.
    4. Xu, Wei, 2014. "Parameter estimation in two-type continuous-state branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 124-134.
    5. Mátyás Barczy & Zenghu Li & Gyula Pap, 2016. "Moment Formulas for Multitype Continuous State and Continuous Time Branching Process with Immigration," Journal of Theoretical Probability, Springer, vol. 29(3), pages 958-995, September.
    6. Ma, Rugang, 2014. "Stochastic equations for two-type continuous-state branching processes with immigration and competition," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 83-89.
    7. Sato, Ken-iti & Yamazato, Makoto, 1984. "Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type," Stochastic Processes and their Applications, Elsevier, vol. 17(1), pages 73-100, May.
    8. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    9. Aurélien Alfonsi, 2015. "Affine Diffusions and Related Processes: Simulation, Theory and Applications," Post-Print hal-03127212, HAL.
    10. Mayerhofer, Eberhard & Stelzer, Robert & Vestweber, Johanna, 2020. "Geometric ergodicity of affine processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4141-4173.
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