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