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- Title
Regularity of Harmonic functions for a class of singular stable-like processes.
- Authors
Bass, Richard; Zhen-Qing Chen
- Abstract
We consider the system of stochastic differential equations where Z , . . . , Z are independent one-dimensional symmetric stable processes of order α, and the matrix-valued function A is bounded, continuous and everywhere non-degenerate. We show that bounded harmonic functions associated with X are Hölder continuous, but a Harnack inequality need not hold. The Lévy measure associated with the vector-valued process Z is highly singular.
- Subjects
HARMONIC functions; STOCHASTIC differential equations; OPERATOR algebras; MATRICES (Mathematics); SYMMETRIC domains
- Publication
Mathematische Zeitschrift, 2010, Vol 266, Issue 3, p489
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-009-0581-0