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

Let N_t=e^{i\lambda M_t +\frac{1}{ . The process (M_t)_{t \ge 0} is a standard Brownian motion. Volume 293, Grundlehren der mathematischen Wissenschaften. Moreover, every continuous martingale is just brownian motion with a different clock. Author: Daniel Revuz, Marc Yor Type: eBook. Yor, Continuous Martingales and Brownian Motion, Third Edition Corrected. Product Description PThis is a magnificent book! [ReYo98] D.Revuz, M.Yor, Continuous Martingales and Brownian Motion, Grundlehren der mathematischen Wissenschaften, 3rd edition, Springer, 1998. 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. Be a continuous local martingale such that M_0=0 and such that for every t \ge 0 , \langle M \rangle_t =t . Brownian Motion and Martingales in Continuous Time Wiley: Introduction to Probability and Stochastic Processes with. Language: English Released: 2004. Continuous martingales and Brownian motion. Whence, the entire theory of stochastic calculus is built around brownian motion. GO Continuous martingales and Brownian motion. 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. 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.