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Potential Analysis

, Volume 40, Issue 4, pp 539–563 | Cite as

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

  • R. MikuleviciusEmail author
  • H. Pragarauskas
Article

Abstract

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.

Keywords

Non-local parabolic equations Hölder-Zygmund spaces Lévy processes Martingale problem 

Mathematics Subject Classifications (2010)

45K05 60J75 35B65 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.University of Southern CaliforniaLos AngelesUSA
  2. 2.Institute of Mathematics and InformaticsVilnius UniversityVilniusLithuania

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