Mwigilwa, WinfridaAduda, JaneLe Doux Mbele, Bidima MartinKube, Ananda2023-06-082023-06-082022Mwigilwa, W., Aduda, J., Mbele, B.M.L.D. and Kube, A. (2022) Different Types of Structure Conditions of Semimartingale with Jacod Decomposition. Journal of Mathematical Finance , 12, 367-381. https://doi.org/10.4236/jmf.2022.1220212162-2442http://ir-library.ku.ac.ke/handle/123456789/25723research articleThe 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.enStructure Condition (SC)Minimal Structure Condition (MSC)Natural Structure Condition (NSC)Jacod DecompositionArticle