Regularity of harmonic functions for a class of singular stable-like processes (Q707559)

From the authors' abstract: We consider the system of stochastic differential equations \[ dX_t=A(X_{t-})\, dZ_t, \] where \(Z_t^1 , \dots , Z_t^d\) are independent one-dimensional symmetric stable processes of order \(\alpha \), 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.