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Let U be an open set in R^d. We show that under a mild assumption on therichness of the generator a Feller process in U with (predictable) killing is asemimartingale. To this end we generalize the notion of semimartingales in anatural way to those 'with killing'. Furthermore we calculate thesemimartingale characteristics of the Feller process explicitly and analyzetheir connections to the symbol. Finally we derive a probabilistic formula tocalculate the symbol of the process directly.

On the Semimartingale Nature of Feller Processes with Killing