Some Aspects of Brownian Motion

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Focusing on martingales and stochastic calculus, this book serves as a follow-up to earlier lectures on Brownian motion. It delves into advanced techniques that enhance the computation of interesting functionals introduced in Part I. The author reflects on the evolution of research in this field, likening it to gold mining, where modern technology plays a crucial role in uncovering rewards. The content includes discussions on stochastic calculus for discontinuous semi-martingales and the enlargement of filtrations, emphasizing the sophistication of contemporary methods.