ABSTRACT
This chapter presents optional and predictable projections of measurable processes, dual optional and predictable projection of processes with finite variation. As an application of projection theory, It shows the extremely important Doob-Meyer decomposition theorem for supermartingales. The chapter gives a detailed discussion about nitrations of discrete type to conclude the general theory of stochastic processes. It provides theorems and lemmas for projections of processes such as projections of measurable processes and dual projections of increasing processes. The chapter explains Doob-Meyer decomposition theorem and focuses on discrete type filtrations.
