On the semimartingale nature of Feller processes with killing

被引：13

作者：

Schnurr, Alexander ^{[1
]}

机构：

[1] Tech Univ Dortmund, Fak Math, Lehrstuhl 4, D-44227 Dortmund, Germany

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2012年 / 122卷 / 07期

关键词：

Semimartingale; Killed process; Feller semigroup; Negative definite symbol; OPERATORS; SYMBOLS;

D O I：

10.1016/j.spa.2012.04.009

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：2758 / 2780

页数：23

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