ABSTRACT
This chapter discusses local martingales in the semimartingale theory and stochastic calculus. It explains localization of classes of processes, decomposition of local martingales, and jumps of local martingales. The chapter presents theorems and lemmas for the localization of classes of processes, decomposition of local martingales, and jumps of local martingales. The theorems are the fundamental theorem for local martingales. It plays an important role in the theory of local martingales.
