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Coupling and strong Feller for jump processes on Banach spaces

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  • Wang, Feng-Yu
  • Wang, Jian

Abstract

By using lower bound conditions of the Lévy measure w.r.t. a nice reference measure, the coupling and strong Feller properties are investigated for the Markov semigroup associated with a class of linear SDEs driven by (non-cylindrical) Lévy processes on a Banach space. Unlike in the finite-dimensional case where these properties have also been confirmed for Lévy processes without drift, in the infinite-dimensional setting the appearance of a drift term is essential to ensure the quasi-invariance of the process by shifting the initial data. Gradient estimates and exponential convergence are also investigated. The main results are illustrated by specific models on the Wiener space and separable Hilbert spaces.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:5:p:1588-1615
    DOI: 10.1016/j.spa.2013.01.004
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    References listed on IDEAS

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    1. Zhang, Xicheng, 2013. "Derivative formulas and gradient estimates for SDEs driven by α-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1213-1228.
    2. Cranston, Michael & Greven, Andreas, 1995. "Coupling and harmonic functions in the case of continuous time Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 261-286, December.
    3. Wang, Feng-Yu, 2011. "Gradient estimate for Ornstein-Uhlenbeck jump processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 466-478, March.
    4. 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.
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