On the semimartingale nature of Feller processes with killing

Let U be an open set in R d . We show that under a mild assumption on the richness of the generator, a Feller process in ( U , B ( U ) ) with (predictable) killing is a semimartingale. To this end, we generalize the notion of semimartingales in a natural way to those ‘with killing’. Furthermore we calculate the semimartingale characteristics of the Feller process explicitly and analyze their connections to the symbol. Finally we derive a probabilistic formula for calculating the symbol of the process.