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Regularity of transition densities and ergodicity for affine jump‐diffusions

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Listed:
  • Martin Friesen
  • Peng Jin
  • Jonas Kremer
  • Barbara Rüdiger

Abstract

This paper studies the transition density and exponential ergodicity for affine processes on the canonical state space R≥0m×Rn$\mathbb {R}_{\ge 0}^{m}\times \mathbb {R}^{n}$. Under a Hörmander‐type condition for diffusion components as well as a boundary nonattainment condition, we derive the existence and regularity of the transition densities and then prove the strong Feller property of the associated semigroup. Moreover, we also show that, under an additional subcriticality condition on the drift, the corresponding affine process is exponentially ergodic in the total variation distance.

Suggested Citation

  • Martin Friesen & Peng Jin & Jonas Kremer & Barbara Rüdiger, 2023. "Regularity of transition densities and ergodicity for affine jump‐diffusions," Mathematische Nachrichten, Wiley Blackwell, vol. 296(3), pages 1117-1134, March.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:3:p:1117-1134
    DOI: 10.1002/mana.202000299
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    References listed on IDEAS

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    1. Filipović, Damir & Mayerhofer, Eberhard & Schneider, Paul, 2013. "Density approximations for multivariate affine jump-diffusion processes," Journal of Econometrics, Elsevier, vol. 176(2), pages 93-111.
    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.
    3. Li, Zenghu & Ma, Chunhua, 2015. "Asymptotic properties of estimators in a stable Cox–Ingersoll–Ross model," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3196-3233.
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