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Stochastic Calculus: An Introduction with Applications. 3.2 Stochastic integral.A Continuous Local Martingales as Stochastic Integrals with Respect to Brownian Motion. 170:. Brownian motion and stochastic calculus Ioannis Karatzas, Steven E.TIME SERIES ECONOMETRICS II UNIT ROOTS AND COINTEGRATION. Kopp P. E. (1984). Martingales and Stochastic. P. (1990). Stochastic Integration and Differential.This book provides an introduction to the rapidly expanding theory of stochastic integration and martingales.Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and Their Applications, 11, 215-260.Stochastic Calculus Notes, Lecture 5 Last modi ed October 24, 2002 1 Continuous time martingales.