From Markov processes to semimartingales

In the development of stochastic integration and theory semimartingales, Markov processes have been a constant source inspiration. Despite this historical interweaving, it turned out that semimartingales should be considered ‘natural’ class for many concepts first developed in Markovian framework. As an example, differential equations invented as tool to study but nowadays are treated separately literature. Moreover, killing has known decades before made its way most recently. We describe, when these other important how they where transferred semimartingales. Further topics include symbol, characteristics generalizations Blumenthal-Getoor indices. Some additional comments on relations between round paper.