Levy driven moving averages and semimartingales

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Basse, Andreas¹  Pedersen, Jan¹ 

[1] Univ Aarhus, Dept Math Sci, DK-8000 Aarhus C, Denmark

关键词: Semimartingales;    Moving averages;    Levy processes;    Bounded variation;    Absolutely continuity;    Stable processes;    Fractional processes;   

DOI  :  10.1016/j.spa.2009.03.007

来源: Elsevier

【 摘 要 】

The aim of the present paper is to study the semimartingale property of continuous time moving averages driven by Levy processes. We provide necessary and sufficient conditions on the kernel for the moving average to be a semimartingale in the natural filtration of the Levy process, and when this is the case we also provide a useful representation. Assuming that the driving Levy process is of unbounded variation, we show that the moving average is a semimartingale if and only if the kernel is absolutely continuous with a density satisfying an integrability condition. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free