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xorshammer.com | ||
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almostsuremath.com
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| | | | | In this post I attempt to give a rigorous definition of integration with respect to Brownian motion (as introduced by Itô in 1944), while keeping it as concise as possible. The stochastic integral can also be defined for a much more general class of processes called semimartingales. However, as Brownian motion is such an important... | |
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almostsuremath.com
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| | | | | I start these notes on stochastic calculus with the definition of a continuous time stochastic process. Very simply, a stochastic process is a collection of random variables $latex {\{X_t\}_{t\ge 0}}&fg=000000$ defined on a probability space $latex {(\Omega,\mathcal{F},{\mathbb P})}&fg=000000$. That is, for each time $latex {t\ge 0}&fg=000000$, $latex {\omega\mapsto X_t(\omega)}&fg=000000$ is a measurable function from $latex... | |
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homotopytypetheory.org
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| | | | | In this blog post I would like to approach dependendent types from a presheaf point of view. This allows us to take the theory of presheaves as an inspiration for results in homotopy type theory. The first result from this direction is a type theoretical variant of the Yoneda lemma, stating that the fiber $latex... | |
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cyclostationary.blog
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| | | Our toolkit expands to include basic probability theory. | ||
