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Martingale theory I

Martingale theory I:    • Martingale theory I   Martingale theory II:    • Martingale theory II   Martingale theory III:    • Martingale theory III   Martingale theory IV:    • Martingale theory IV   ____________________________________ Martingale theory: We review basic facts from martingale theory. We start with discretetime parameter martingales and proceed to explain what modifications are needed in order to extend the results from discrete-time to continuous-time. The Doob-Meyer decomposition theorem for continuous semimartingales is stated but the proof is omitted. At the end of the chapter we discuss the quadratic variation process of a local martingale, a key concept in martingale theory based stochastic analysis. ____________________________________