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 language | English |
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Pages (from-to) | 595-610 |
Number of pages | 16 |
Journal | Probability Theory and Related Fields |
Volume | 124 |
Issue number | 4 |
DOIs | |
Publication status | Published - Dec 2002 |
Externally published | Yes |
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