On the Semimartingale Nature of Feller Processes with Killing

Alexander Schnurr

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arXiv · 1008.2279

On the Semimartingale Nature of Feller Processes with Killing

Alexander Schnurr

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Abstract

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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Alexander Schnurr. 2012-05-04. On the Semimartingale Nature of Feller Processes with Killing. https://arxiv.org/abs/1008.2279

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