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Continuous martingales and Brownian motion Daniel Revuz, Marc Yor
Publisher: Springer

Then, to get a solid background in SDE's you can read Revuz, Yor "Continuous Martingales and Brownian Motion" which is more or a less the standard stoch calc book for pure mathematicians. Amazon.com: Handbook of Brownian Motion - Facts and Formulae. Moreover, every continuous martingale is just brownian motion with a different clock. The martingale representation theorem states that any martingale adapted with respect to a Brownian motion can be expressed as a stochastic integral with respect to the same Brownian motion. Brownian Motion and Martingales in Continuous Time Wiley: Introduction to Probability and Stochastic Processes with. Diffusions, Markov Processes, and Martingales: Volume 1. Whence, the entire theory of stochastic calculus is built around brownian motion. Yor : Continuous martingales and Brownian motion. North Holland (Second edition, 1988). Product Description PThis is a magnificent book! Watanabe : Stochastic differential equations and diffusion processes.