On the Cauchy problem for integro-differential operators in Sobolev classes and the martingale problem

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Mikulevicius, R.^1,2  Pragarauskas, H.^1,2 

[1] Univ So Calif, Los Angeles, CA 90089 USA

[2] Univ Vilnius, Inst Math & Informat, Vilnius, Lithuania

关键词: Non-local parabolic integro-differential equations;    Levy processes;    Martingale problem;   

DOI  :  10.1016/j.jde.2013.11.008

来源: Elsevier

【 摘 要 】

The existence and uniqueness in Sobolev spaces of solutions of the Cauchy problem to parabolic integro-differential equation with variable coefficients of the order alpha is an element of (0, 2) is investigated. The principal part of the operator has kernel m(t, x, y)/vertical bar y vertical bar(d+alpha) with a bounded nondegenerate m, Holder 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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free