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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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Generalisation of Strassen's (Kellerer's) Theorem

Let $\mu$ and $\nu$ be two probability measures on $\mathbb R^d$ with finite first movements, i.e. $$\int_{\mathbb R^d}|x|~\mu(dx),\quad \int_{\mathbb R^d}|x|~\nu(dx) \quad <\quad +\infty.$$ $\mu$ a …