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Transition Density Estimates for a Class of Lévy and Lévy-Type Processes

Author

Listed:
  • Viktorya Knopova

    (NAS of Ukraine)

  • René L. Schilling

    (Technische Universität Dresden)

Abstract

We show on- and off-diagonal upper estimates for the transition densities of symmetric Lévy and Lévy-type processes. To get the on-diagonal estimates, we prove a Nash-type inequality for the related Dirichlet form. For the off-diagonal estimates, we assume that the characteristic function of a Lévy(-type) process is analytic, which allows us to apply the complex analysis technique.

Suggested Citation

  • Viktorya Knopova & René L. Schilling, 2012. "Transition Density Estimates for a Class of Lévy and Lévy-Type Processes," Journal of Theoretical Probability, Springer, vol. 25(1), pages 144-170, March.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:1:d:10.1007_s10959-010-0300-0
    DOI: 10.1007/s10959-010-0300-0
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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. Paweł Sztonyk, 2010. "Estimates of Tempered Stable Densities," Journal of Theoretical Probability, Springer, vol. 23(1), pages 127-147, March.
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