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Boundary Harnack Principle for Symmetric Stable Processes

✍ Scribed by Renming Song; Jang-Mei Wu

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
189 KB
Volume
168
Category
Article
ISSN
0022-1236

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✦ Synopsis

In this paper we study potential-theoretic properties of the symmetric :-stable processes (0<:<2): establishing the boundary Harnack principle for ratios of :-harmonic functions on any open sets, identifying the Martin boundary with the Euclidean boundary for open sets with a certain interior fatness property, and extending earlier results on intrinsic ultracontractivity and the conditional gauge theorem to certain open sets.

πŸ“œ SIMILAR VOLUMES

Martin Boundary and Integral Representat
Martin Boundary and Integral Representation for Harmonic Functions of Symmetric Stable Processes
✍ Zhen-Qing Chen; Renming Song πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 399 KB

Martin boundaries and integral representations of positive functions which are harmonic in a bounded domain D with respect to Brownian motion are well understood. Unlike the Brownian case, there are two different kinds of harmonicity with respect to a discontinuous symmetric stable process. One kind

Intrinsic Ultracontractivity and Conditi
Intrinsic Ultracontractivity and Conditional Gauge for Symmetric Stable Processes
✍ Zhen-Qing Chen; Renming Song πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 456 KB

It is shown in this paper that the conditional gauge theorem holds for symmetric :-stable processes on bounded C 1, 1 domains in R n where 0<:<2 and n 2. Two of the major tools used to prove this conditional gauge theorem are logarithmic Sobolev inequality and intrinsic ultracontractivity. ## 1997

Large deviations for discontinuous addit
Large deviations for discontinuous additive functionals of symmetric stable processes
✍ Masayoshi Takeda; Kaneharu Tsuchida πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 227 KB

## Abstract Let __X~t~__ be a symmetric stable process on __d__‐dimensional Euclidean space \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb {R}}^d$\end{document}. Let __F__(__x__, __y__) be a symmetric positive bounded function on \documentclass{article}\usepac