Boundary Harnack principle for subordinate Brownian motions
By Panki Kim, Renming Song, Zoran Vondraček. 2007
61 citations recorded by the source corpus.
We establish a boundary Harnack principle for a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in [kappa]-fat open sets (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded [kappa]-fat open sets with respect to these processes with their Euclidean boundaries.
Subfields: Applied Mathematics, Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/72dad02f751869844235f58bad6240d101208939
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In Applied Mathematics
- Renming Song
- Panki Kim
- Zoran Vondraček
- M. Ryznar
- Mateusz Kwaśnicki
- Krzysztof Bogdan
- J. Małecki
- Zhen-Qing Chen
In Finance
- Renming Song
- Panki Kim
- M. Ryznar
- Zoran Vondraček
- Mateusz Kwaśnicki
- J. Małecki
- Zhen-Qing Chen
- Krzysztof Bogdan
In Mathematical Physics
- Renming Song
- Panki Kim
- Zoran Vondraček
- Mateusz Kwaśnicki
- M. Ryznar
- J. Małecki
- Zhen-Qing Chen
- Krzysztof Bogdan
Citations in the corpus
- Two‐sided Green function estimates for killed subordinate Brownian motions (2010, methodology): “One difference to the current setting was that in [20] the Laplace exponent was assumed to be precisely regularly varying at infinity and not just comparable to a regularly varying function.”
- Suprema of Lévy processes (2011, methodology): “The recent progress in the potential theory of Lévy processes is, in part, due to the application of fluctuation theory, see [9, 10, 18, 22, 23, 24, 25].”
- Boundary Harnack inequality for Markov processes with jumps (2012, unknown): “Vondraček proved BHI for subordinate Brownian motions in fat sets ([63]) and in 2011 extended it to a general class of isotropic Lévy processes and arbitrary domains ([65]).”
- Uniform boundary Harnack principle for rotationally symmetric Lévy processes in general open sets (2011, background): “In [8] the boundary Harnack principle was established for harmonic functions with respect to a wide class of purely discontinuous subordinate Brownian motions in κ-fat open sets, with an extension obtained in [10].”