Nonlocal elliptic equation in Hölder space and the martingale problem

Abstract

The well-posedness of nonlocal elliptic equation with singular drift is investigated in Besov-Hölder spaces. As an application of our main analytic results, we show the existence and uniqueness for corresponding martingale problem. Moreover, we prove that the one dimensional distribution of the martingale solution has a density in certain Besov space.