On the Semimartingale Nature of Feller Processes with Killing

Details On the Semimartingale Nature of Feller Processes with Killing On the Semimartingale Nature of Feller Processes with Killing

2010-08-13

arxiv.org/abs/1008.2279v1

Mathematics

Probability

Scientific paper

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 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 to calculate the symbol of the process directly.

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