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Dellacherie, C. and Meyer, P. (1982) Probabilities and Potential B: Theory of Martingales. North-Holland Mathematics Studies, Vol. II, North-Holland, Amsterdam.

has been cited by the following article:

• TITLE: Different Types of Structure Conditions of Semimartingale with Jacod Decomposition

  AUTHORS: Winfrida Mwigilwa, Jane Aduda, Bidima Martin Le Doux Mbele, Ananda Kube

  KEYWORDS: Structure Condition (SC), Minimal Structure Condition (MSC), Natural Struc-ture Condition (NSC), Jacod Decomposition

  JOURNAL NAME: Journal of Mathematical Finance, Vol.12 No.2, May 26, 2022

  ABSTRACT: 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.