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On the semimartingale nature of Feller processes with killing

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  • Schnurr, Alexander

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.

Suggested Citation

  • Schnurr, Alexander, 2012. "On the semimartingale nature of Feller processes with killing," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2758-2780.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:7:p:2758-2780
    DOI: 10.1016/j.spa.2012.04.009
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    Cited by:

    1. Irmina Czarna & Adam Kaszubowski, 2020. "Optimality of Impulse Control Problem in Refracted Lévy Model with Parisian Ruin and Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 982-1007, June.

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