Different Types of Structure Conditions of Semimartingale with Jacod Decomposition

View/ Open
Date
2022Author
Mwigilwa, Winfrida
Aduda, Jane
Le Doux Mbele, Bidima Martin
Kube, Ananda
Metadata
Show full item recordAbstract
The objective of this article is to use Jacod decomposition to develop different
types of semimartingale structure conditions. We make the following contributions
to that end: When a continuous semimartingale meets the structure
condition (SC), we prove that there is a minimal martingale density and a
predictable variation part. When a special semimartingale meets the minimal
structure condition (MSC) and the natural structure condition (NSC), we derive
a Radon-Nikodym decomposition and a Natural Kunita-Watanabe decomposition
from a given sigma martingale density, which is written under
the Jacod decomposition.