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The reader would have noticed that in the development of stochastic integration in the previous chapter, we have not talked about either martingales or semimartingales. A semimartingale is any process which can be written as a sum of a local martingale and a process with finite variation paths. The main theme of this chapter is to show that the class of stochastic integrators is the same as the class of semimartingales, thereby showing that stochastic integral is defined for all semimartingales and the Ito formula holds for them. This is the Dellacherie–Meyer–Mokobodzky–Bichteler Theorem.