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

The process (M_t)_{t ge 0} is a standard Brownian motion. Product Description PThis is a magnificent book! Volume 293, Grundlehren der mathematischen Wissenschaften. Be a continuous local martingale such that M_0=0 and such that for every t ge 0 , langle M angle_t =t . Continuous Martingales and Brownian Motion (Grundlehren Der Mathematischen Wissenschaften, Vol 293). [7] [法] Daniel Revuz, Marc Yor, Continuous Martingales and Brownian Motion (Grundlehren der. 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. 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. In this book, which is basically self-contained, the following topics are treated thoroughly: Brownian motion as a Gaussian process, Brownian motion as a Markov process, and Brownian motion as a Continuous Distributions - Probability Examples c-6 Related topics which are treated include Markov chains, renewal theory, the martingale problem, Itô calculus, cylindrical measures, and ergodic theory. Description for Contuous Martgales and Brownian Motion REPOST. 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, Third Edition Corrected. Mathematischen Wissenschaften),Springer-Verlag, 3 edition ,January 15, 1999, ￥106.00$.