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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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martingale representation type result

Suppose we have two (not necessarily independent) semimartingales $X$ and $Y$. Let $\mathcal{F}_t$ be the completed filtration generated by $(X_t, Y_t)$ and let $H_t$ be a martingale with respect to $ …
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