Abstract This paper is devoted to the study of a certain type of martingale problems associated to general operators corresponding to processes which have finite lifetime. We analyse several properties and in particular the weak convergence of sequences of solutions for an appropriate Skorokhod topology setting. We point out the Feller-type features of the associated solutions to this type of martingale problem. Then localisation theorems for well-posed martingale problems or for corresponding generators are proved.

中文翻译：

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局部 Feller 过程和鞅局部问题

摘要 本文致力于研究与具有有限生命周期的过程对应的一般算子相关的某种类型的鞅问题。我们分析了几个属性，特别是针对适当的 Skorokhod 拓扑设置的解决方案序列的弱收敛性。我们指出了这类鞅问题的相关解的 Feller 型特征。然后证明了适定鞅问题或相应生成器的定位定理。