On the Cauchy problem for integro-differential operators in Hölder classes and the uniqueness of the martingale problem
R. Mikulevíčius, Henrikas Pragarauskas · arXiv (Cornell University) · 2011
The existence and uniqueness in Hölder spaces of solutions of the Cauchy problem to parabolic integro-differential equation of the order α\in(0,2) is investigated. The principal part of the operator has kernel m(t,x,y)/|y|^{d+α} with a bounded nondegenerate m, Hölder in x and measurable in y. The result is applied to prove the uniqueness of the corresponding martingale problem.