Regularity of harmonic functions for a class of singular stable-like processes
Abstract
We consider the system of stochastic differential equations dXt=A(Xt-) dZt, where Zt1, ..., Zdt 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 Holder continuous, but a Harnack inequality need not hold. The Levy measure associated with the vector-valued process Z is highly singular.
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