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

Continuous martingales and Brownian motion, Revuz D., Yor M. 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. Whence, the entire theory of stochastic calculus is built around brownian motion. Of facts and formulae associated Brownian motion. [ReYo98] D.Revuz, M.Yor, Continuous Martingales and Brownian Motion, Grundlehren der mathematischen Wissenschaften, 3rd edition, Springer, 1998. The process (M_t)_{t \ge 0} is a standard Brownian motion. Hm, it's covered in Yor's book "Continuous martingales and brownian motion" but only as an exercise, I also believe it's present in "Aspects of brownian motion" but I don't have access to this book as of now. Moreover, every continuous martingale is just brownian motion with a different clock. Let N_t=e^{i\lambda M_t +\frac{1}{ . Brownian Motion and Martingales in Continuous Time Wiley: Introduction to Probability and Stochastic Processes with. Be a continuous local martingale such that M_0=0 and such that for every t \ge 0 , \langle M \rangle_t =t . Probability and its Applications Continuous martingales and brownian motion Continuous martingales and brownian motion,D.