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, 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 some Besov space.

References in corpus (8)

• Well-posedness of the transport equation by stochastic perturbation
• Schauder estimates for a class of non-local elliptic equations
• Real Paley-Wiener theorems and local spectral radius formulas
• Heat kernel and ergodicity of SDEs with distributional drifts
• Uniqueness of stable-like processes
• Schauder estimates in generalized Hölder spaces
• Well-posedness of supercritical SDE driven by Lévy processes with irregular drifts
• Dirichlet problem for supercritical nonlocal operators

Cited by in corpus (4)

• Multidimensional SDE with distributional drift and Lévy noise
• Schauder's estimates for nonlocal equations with singular Lévy measures
• Regularity properties of jump diffusions with irregular coefficients
• Weak well-posedness for degenerate SDEs driven by Lévy processes