Insights Brownian Motions and Quantifying Randomness in Physical Systems

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Stochastic calculus has evolved significantly since Robert Brown's 1827 observations of pollen motion, becoming essential in fields like data science, quantitative finance, and mathematical biology. The article discusses Brownian processes and their applications, including a relatable example involving a "drunken martingale." It also touches on stochastic differential equations without delving into complex mathematical details. The insights aim to make the concepts accessible to a broader audience. Overall, the discussion highlights the relevance of Brownian motion in understanding randomness in physical systems.
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Stochastic calculus has come a long way since Robert Brown described the motion of pollen through a microscope in 1827. It’s now a key player in data science, quant finance, and mathematical biology. This article is drawn from notes I wrote for an undergraduate statistical physics course a few months ago. There won’t be any mathematical rigor.

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ToggleBrownian processes (and a Wetherspoons customer)Example: A drunken martingaleStochastic differential equations...


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