On the Cauchy problem for integro-differential operators in Hölder classes and the uniqueness of the martingale problem

2011/03/17 by R. Mikulevicius, Mikulevicius, R., H. Pragarauskas +1
Mathematics · #35B65 #45K05 #60J75 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR #msc:35B65 #msc:45K05 #msc:60J75

paper · pdf · doi:10.48550/arxiv.1103.3492

arxiv created 2011/08/12 · arxiv updated 2011/08/15

Abstract

The existence and uniqueness in Hölder spaces of 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.

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