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. Whence, the entire theory of stochastic calculus is built around brownian motion. Volume 293, Grundlehren der mathematischen Wissenschaften. Brownian Motion and Martingales in Continuous Time Wiley: Introduction to Probability and Stochastic Processes with. 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. Moreover, every continuous martingale is just brownian motion with a different clock. Description for Contuous Martgales and Brownian Motion REPOST. Yor, Continuous Martingales and Brownian Motion, Third Edition Corrected. [ReYo98] D.Revuz, M.Yor, Continuous Martingales and Brownian Motion, Grundlehren der mathematischen Wissenschaften, 3rd edition, Springer, 1998. Product Description PThis is a magnificent book! Let N_t=e^{ilambda M_t +rac{1}{ . The process (M_t)_{t ge 0} is a standard 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 .