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On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes

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  • Deng, Chang-Song
  • Schilling, René L.

Abstract

We show that shift Harnack type inequalities (in the sense of Wang (2014)) are preserved under Bochner’s subordination. The proofs are based on two types of moment estimates for subordinators. As a by-product we establish moment estimates for general Lévy processes.

Suggested Citation

  • Deng, Chang-Song & Schilling, René L., 2015. "On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3851-3878.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:10:p:3851-3878
    DOI: 10.1016/j.spa.2015.05.013
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    Cited by:

    1. Fageot, Julien & Fallah, Alireza & Unser, Michael, 2017. "Multidimensional Lévy white noise in weighted Besov spaces," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1599-1621.
    2. Kühn, Franziska & Schilling, René L., 2019. "Strong convergence of the Euler–Maruyama approximation for a class of Lévy-driven SDEs," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2654-2680.
    3. Chang-Song Deng, 2020. "Subgeometric Rates of Convergence for Discrete-Time Markov Chains Under Discrete-Time Subordination," Journal of Theoretical Probability, Springer, vol. 33(1), pages 522-532, March.
    4. Song, Yan-Hong, 2016. "Algebraic ergodicity for SDEs driven by Lévy processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 108-115.
    5. Kühn, Franziska, 2017. "Existence and estimates of moments for Lévy-type processes," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 1018-1041.
    6. Julien Fageot & Michael Unser, 2019. "Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Lévy White Noises," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1166-1189, September.
    7. Grahovac, Danijel, 2022. "Intermittency in the small-time behavior of Lévy processes," Statistics & Probability Letters, Elsevier, vol. 187(C).
    8. Iosif Pinelis, 2018. "Positive-part moments via characteristic functions, and more general expressions," Journal of Theoretical Probability, Springer, vol. 31(1), pages 527-555, March.
    9. Robin Merkle & Andrea Barth, 2023. "On Properties and Applications of Gaussian Subordinated Lévy Fields," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-33, June.

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