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

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