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Constructions of coupling processes for Lévy processes

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  • Böttcher, Björn
  • Schilling, René L.
  • Wang, Jian

Abstract

We construct optimal Markov couplings of Lévy processes, whose Lévy (jump) measure has an absolutely continuous component. The construction is based on properties of subordinate Brownian motions and the coupling of Brownian motions by reflection.

Suggested Citation

  • Böttcher, Björn & Schilling, René L. & Wang, Jian, 2011. "Constructions of coupling processes for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1201-1216, June.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:6:p:1201-1216
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    References listed on IDEAS

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    1. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
    2. Wang, Feng-Yu, 2011. "Gradient estimate for Ornstein-Uhlenbeck jump processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 466-478, March.
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    Cited by:

    1. Luo, Dejun & Wang, Jian, 2019. "Refined basic couplings and Wasserstein-type distances for SDEs with Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3129-3173.
    2. Fomichov, Vladimir & González Cázares, Jorge & Ivanovs, Jevgenijs, 2021. "Implementable coupling of Lévy process and Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 407-431.
    3. Jianhai Bao & Jian Wang, 2023. "Coupling methods and exponential ergodicity for two‐factor affine processes," Mathematische Nachrichten, Wiley Blackwell, vol. 296(5), pages 1716-1736, May.
    4. Jian Wang, 2014. "On the Existence and Explicit Estimates for the Coupling Property of Lévy Processes with Drift," Journal of Theoretical Probability, Springer, vol. 27(3), pages 1021-1044, September.
    5. Wang, Feng-Yu & Wang, Jian, 2013. "Coupling and strong Feller for jump processes on Banach spaces," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1588-1615.
    6. Majka, Mateusz B., 2017. "Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 4083-4125.

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