In this paper we discuss the new stochastic integral in  in terms of the Itô isometry. We prove the Doob-Meyer decomposition theorem for near-submartingales in the classes (D) and (DL): Moreover, we introduce a stochastic integral by a near-martingale as an application of the decomposition theorem.
Publication Source (Journal or Book title)
Communications on Stochastic Analysis
Hibino, S., Kuo, H., & Saitô, K. (2018). A stochastic integral by a near-martingale. Communications on Stochastic Analysis, 12 (2), 197-213. https://doi.org/10.31390/cosa.12.2.07