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Brownian Motion and Stochastic CalculusA graduate course text, written for readers familiar with measure theoretic probability and discrete time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by

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