On the semimartingale nature of Feller processes with killing

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Schnurr, Alexander

关键词: Semimartingale;    Killed process;    Feller semigroup;    Negative definite symbol;   

DOI  :  10.1016/j.spa.2012.04.009

来源: Elsevier

【 摘 要 】

Let U he an open set in R-d. 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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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