Regularity of solutions to anisotropic nonlocal equations

We study harmonic functions associated to systems of stochastic differential equations of the form $d{X}_t^i=A_{i1}(X_{t-})d{Z}_t^1+\cdots +A_{id}(X_{t-})d{Z}_t^d$, $i\in \{1,\dots ,d\}$, where $Z_t^j$ are independent one-dimensional symmetric stable processes with indices ${\alpha }_j\in (0,2)$, $j\in \{1,\dots ,d\}$. In this article we prove H"older regularity of bounded harmonic functions with respect to solutions to such systems.