On the Cauchy Problem for Integro-differential Operators in Hölder Classes and the Uniqueness of the Martingale Problem

被引：0

作者：

R. Mikulevicius

H. Pragarauskas

机构：

[1] University of Southern California,Institute of Mathematics and Informatics

[2] Vilnius University,undefined

来源：

Potential Analysis | 2014年 / 40卷

关键词：

Non-local parabolic equations; Hölder-Zygmund spaces; Lévy processes; Martingale problem; 45K05; 60J75; 35B65;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The existence and uniqueness in Hölder spaces of classical solutions of the Cauchy problem to parabolic integro-differential equation of the order α ∈ (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.

引用

页码：539 / 563

页数：24

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