On the semimartingale nature of Feller processes with killing

Alexander Schnurr

Stochastic Processes and their Applications, 2012, vol. 122, issue 7, 2758-2780

Abstract: Let U be an open set in Rd. 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.

Keywords: Semimartingale; Killed process; Feller semigroup; Negative definite symbol (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:7:p:2758-2780

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DOI: 10.1016/j.spa.2012.04.009

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