Acta Applicandae Mathematicae

, Volume 146, Issue 1, pp 113–143

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


DOI: 10.1007/s10440-016-0061-6

Cite this article as:
Chen, ZQ. & Kim, P. Acta Appl Math (2016) 146: 113. doi:10.1007/s10440-016-0061-6


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.


Dirichlet heat kernel Transition density Survival probability Exit time Lévy system Lévy process Symmetric Lévy process 

Mathematics Subject Classification (2000)

60J35 47G20 60J75 47D07 

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Department of Mathematical Sciences and Research Institute of MathematicsSeoul National UniversitySeoulRepublic of Korea

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