Brownian Motions and Quantifying Randomness in Physical Systems

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SUMMARY

The discussion centers on the application of stochastic calculus in understanding Brownian motion, a concept first described by Robert Brown in 1827. It highlights the relevance of Brownian processes in fields such as data science, quantitative finance, and mathematical biology. The article serves as an introductory resource for undergraduate students studying statistical physics, emphasizing practical examples over mathematical rigor.

PREREQUISITES
  • Understanding of stochastic calculus
  • Familiarity with Brownian motion concepts
  • Basic knowledge of statistical physics
  • Awareness of applications in quantitative finance
NEXT STEPS
  • Explore stochastic differential equations in depth
  • Study applications of Brownian motion in quantitative finance
  • Investigate the role of stochastic calculus in data science
  • Learn about martingales and their significance in probability theory
USEFUL FOR

This discussion is beneficial for students in statistical physics, data scientists, quantitative analysts, and anyone interested in the mathematical modeling of 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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