Regularity of solutions to anisotropic nonlocal equations

Abstract

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 Hölder regularity of bounded harmonic functions with respect to solutions to such systems.

18 pages

References in corpus (1)

• The martingale problem for a class of nonlocal operators of diagonal type

Cited by in corpus (2)

• Ergodicity of Lévy-driven SDEs arising from multiclass many-server queues
• Regularity estimates for fractional orthotropic $p$-Laplacians of mixed order