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Stochastic calculus provides a consistent theory of integration for stochastic processes and is used to model random systems. Its applications range from statistical physics to quantitative finance.

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Intuition and/or visualisation of Itô integral/Itô's lemma

Suppose you ask a physicist, if a particle is at x = t^2. Now you ask him where the particle is an arbitrarily small time just before t = 1. Physicists always just do a Taylor expansion around the …
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