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Global Dirichlet Heat Kernel Estimates for Symmetric Lévy Processes in Half-Space

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Abstract

In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels of a large class of symmetric (but not necessarily rotationally symmetric) Lévy processes on half spaces for all \(t>0\). These Lévy processes may or may not have Gaussian component. When Lévy density is comparable to a decreasing function with damping exponent \(\beta\), our estimate is explicit in terms of the distance to the boundary, the Lévy exponent and the damping exponent \(\beta\) of Lévy density.

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Acknowledgement

We thank the referees for helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Zhen-Qing Chen

  2. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea

    Panki Kim

Authors
  1. Zhen-Qing Chen
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  2. Panki Kim
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Corresponding author

Correspondence to Panki Kim.

Additional information

Research of Zhen-Qing Chen was partially supported by NSF Grant DMS-1206276. This work of Panki Kim was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2013R1A2A2A01004822).

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Chen, ZQ., Kim, P. Global Dirichlet Heat Kernel Estimates for Symmetric Lévy Processes in Half-Space. Acta Appl Math 146, 113–143 (2016). https://doi.org/10.1007/s10440-016-0061-6

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  • DOI: https://doi.org/10.1007/s10440-016-0061-6

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