Green function estimate for censored stable processes

Zhen Qing Chen*, Panki Kim

*Corresponding author for this work

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Abstract

Sharp two-sided estimates for Green functions of censored α-stable process Y in a bounded C1,1 open set D are obtained, where α ∈ (1, 2). It is shown that the Martin boundary and minimal Martin boundary of Y can all be identified with the Euclidean boundary ∂ D of D. Sharp two-sided estimates for the Martin kernel of Y are also derived.

Original languageEnglish
Pages (from-to)595-610
Number of pages16
JournalProbability Theory and Related Fields
Volume124
Issue number4
DOIs
Publication statusPublished - Dec 2002
Externally publishedYes

Keywords

  • Capacity
  • Censored stable process
  • Green function
  • Harmonic function
  • Martin boundary
  • Martin kernel

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Chen, Z. Q., & Kim, P. (2002). Green function estimate for censored stable processes. Probability Theory and Related Fields, 124(4), 595-610. https://doi.org/10.1007/s00440-002-0226-2