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

[ReYo98] D.Revuz, M.Yor, Continuous Martingales and Brownian Motion, Grundlehren der mathematischen Wissenschaften, 3rd edition, Springer, 1998. Brownian Motion and Martingales in Continuous Time Wiley: Introduction to Probability and Stochastic Processes with. Let N_t=e^{ilambda M_t +rac{1}{ . Whence, the entire theory of stochastic calculus is built around brownian motion. Continuous Martingales and Brownian Motion (Grundlehren Der Mathematischen Wissenschaften, Vol 293). Moreover, every continuous martingale is just brownian motion with a different clock. 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. Be a continuous local martingale such that M_0=0 and such that for every t ge 0 , langle M angle_t =t . 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. May 16, 2011- Probability Reading Group, Warwick - "Local times" based on the book "Continuous martingales and Brownian motion" by D. Amazon.com: Handbook of Brownian Motion - Facts and Formulae. Diffusions, Markov Processes, and Martingales: Volume 1. The process (M_t)_{t ge 0} is a standard Brownian motion.