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Estimates of Dirichlet heat kernels for unimodal Lévy processes with low intensity of small jumps. (English) Zbl 1480.60221

The authors study transition density functions for pure jump unimodal Lévy processes killed upon leaving an open set \(D\). Their result covers the case that the Lévy densities of unimodal Lévy processes are regularly varying functions whose indices are equal to the Euclidean dimension. This is the first result on two-sided Dirichlet heat kernel estimates for Lévy processes such that the weak lower scaling index of the Lévy densities is not necessarily strictly bigger than the Euclidean dimension.

MSC:

60J35 Transition functions, generators and resolvents
60G51 Processes with independent increments; Lévy processes
60J50 Boundary theory for Markov processes
60J76 Jump processes on general state spaces
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References:

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