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

Of facts and formulae associated Brownian motion. Watanabe : Stochastic differential equations and diffusion processes. Diffusions, Markov Processes, and Martingales: Volume 1. 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. Download Continuous Martingales and Brownian Motion Revuz, M. Continuous Martingales and Brownian Motion (Grundlehren Der Mathematischen Wissenschaften, Vol 293). Whence, the entire theory of stochastic calculus is built around brownian motion. Be a continuous local martingale such that M_0=0 and such that for every t ge 0 , langle M angle_t =t . 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. Let N_t=e^{ilambda M_t +rac{1}{ . Yor : Continuous martingales and Brownian motion. Probability and its Applications Continuous martingales and brownian motion Continuous martingales and brownian motion,D. Continuous martingales and Brownian motion, Revuz D., Yor M. Amazon.com: Handbook of Brownian Motion - Facts and Formulae. Moreover, every continuous martingale is just brownian motion with a different clock. 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. Continuous Martingales and Brownian Motion book download. North Holland (Second edition, 1988). May 16, 2011- Probability Reading Group, Warwick - "Local times" based on the book "Continuous martingales and Brownian motion" by D.