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Affine Jump-Diffusions: Stochastic Stability and Limit Theorems

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  • Xiaowei Zhang
  • Peter W. Glynn

Abstract

Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require ergodicity in order establish consistency and asymptotic normality of the associated estimators. In this paper, we develop stochastic stability conditions for affine jump-diffusions, thereby providing the needed large-sample theoretical support for estimating such processes. We establish ergodicity for such models by imposing a `strong mean reversion' condition and a mild condition on the distribution of the jumps, i.e. the finiteness of a logarithmic moment. Exponential ergodicity holds if the jumps have a finite moment of a positive order. In addition, we prove strong laws of large numbers and functional central limit theorems for additive functionals for this class of models.

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  • Xiaowei Zhang & Peter W. Glynn, 2018. "Affine Jump-Diffusions: Stochastic Stability and Limit Theorems," Papers 1811.00122, arXiv.org.
    • Handle: RePEc:arx:papers:1811.00122
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    Cited by:

    1. 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.
    2. 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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