On the Cauchy problem for integro-differential operators in Sobolev classes and the martingale problem
Analysis of PDEs
2012-01-24 v4 Probability
Abstract
The existence and uniqueness in Sobolev spaces of solutions of the Cauchy problem to parabolic integro-differential equation of the order {\alpha}\in(0,2) is investigated. The principal part of the operator has kernel m(t,x,y)/|y|^{d+{\alpha}} with a bounded nondegenerate m, H\"older in x and measurable in y. The lower order part has bounded and measurable coefficients. The result is applied to prove the existence and uniqueness of the corresponding martingale problem.
Cite
@article{arxiv.1112.4467,
title = {On the Cauchy problem for integro-differential operators in Sobolev classes and the martingale problem},
author = {R. Mikulevicius and H. Pragarauskas},
journal= {arXiv preprint arXiv:1112.4467},
year = {2012}
}