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On Symmetric Stable-Type Processes with Degenerate/Singular Lévy Densities

Abstract

We consider symmetric stable-type processes with degenerate/singular Lévy densities via Dirichlet form theory. We give conditions of some global path properties of the processes such as recurrence, transience or conservativeness. We also show the polarity of a point.

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Correspondence to Toshihiro Uemura.

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Okamura, H., Uemura, T. On Symmetric Stable-Type Processes with Degenerate/Singular Lévy Densities. J Theor Probab (2020). https://doi.org/10.1007/s10959-020-00990-6

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Keywords

  • Symmetric stable-type processes
  • Recurrence
  • Transience
  • Conservativeness

Mathematics Subject Classification (2010)

  • Primary 31C25
  • Secondary 60J75