Titlebook: Brownian Motion, Martingales, and Stochastic Calculus; Jean-Fran?ois Le Gall Textbook 2016 Springer International Publishing Switzerland 2

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Stochastic Integration,erizing Brownian motion as a continuous local martingale with quadratic variation process equal to ., the Burkholder–Davis–Gundy inequalities and the representation of martingales as stochastic integrals in a Brownian filtration. The end of the chapter is devoted to Girsanov’s theorem, which deals w

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Textbook 2016ownian Motion, Martingales, and Stochastic Calculus.?provides astrong theoretical background to the reader interested in such developments..Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on co

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Gaussian Variables and Gaussian Processes,t Gaussian random variables and Gaussian vectors. We then discuss Gaussian spaces and Gaussian processes, and we establish the fundamental properties concerning independence and conditioning in the Gaussian setting. We finally introduce the notion of a Gaussian white noise, which is used to give a s

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