Martin boundary of unbounded sets for purely discontinuous Feller processes
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Panki Kim
Abstract
In this paper, we study the Martin kernels of general open sets associated with inaccessible points for a large class of purely discontinuous Feller processes in metric measure spaces. Let D be an unbounded open set. Infinity is accessible from D if the expected exit time from D is infinite, and inaccessible otherwise. We prove that under suitable assumptions there is only one Martin boundary point associated with infinity, and that this point is minimal if and only if infinity is accessible from D. Similar results are also proved for finite boundary points of D.
Funding source: National Research Foundation of Korea
Award Identifier / Grant number: NRF-2015R1A4A1041675
Funding source: Simons Foundation
Award Identifier / Grant number: 208236
Funding source: Hrvatska Zaklada za Znanost
Award Identifier / Grant number: 3526
Funding statement: The work of Panki Kim was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2015R1A4A1041675). Renming Song was supported in part by a grant from the Simons Foundation (208236). The research of Zoran Vondraček was supported in part by the Croatian Science Foundation under the project 3526.
Acknowledgements
Part of the research for this paper was done during the visit of Renming Song and Zoran Vondraček to Seoul National University from May 24 to June 8 of 2015. They thank the Department of Mathematical Sciences of Seoul National University for the hospitality.
References
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© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Behavior of bounds of singular integrals for large dimension
- The twofold way of super holonomy
- On mod p singular modular forms
- Martin boundary of unbounded sets for purely discontinuous Feller processes
- Bi-parameter and bilinear Calderón–Vaillancourt theorem with subcritical order
- Nontrivial solutions of superlinear nonlocal problems
- Hopfian $\ell$-groups, MV-algebras and AF~{C}*-algebras
- On regularization of vector distributions on manifolds
- The Addition Theorem for algebraic entropies induced by non-discrete length functions
- When are Zariski chambers numerically determined?
- Convexity theorems for semisimple symmetric spaces
- On amenability of groups generated by homogeneous automorphisms and their cracks
Articles in the same Issue
- Frontmatter
- Behavior of bounds of singular integrals for large dimension
- The twofold way of super holonomy
- On mod p singular modular forms
- Martin boundary of unbounded sets for purely discontinuous Feller processes
- Bi-parameter and bilinear Calderón–Vaillancourt theorem with subcritical order
- Nontrivial solutions of superlinear nonlocal problems
- Hopfian $\ell$-groups, MV-algebras and AF~{C}*-algebras
- On regularization of vector distributions on manifolds
- The Addition Theorem for algebraic entropies induced by non-discrete length functions
- When are Zariski chambers numerically determined?
- Convexity theorems for semisimple symmetric spaces
- On amenability of groups generated by homogeneous automorphisms and their cracks
