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  "body": "\n## Summary\n\nThe Wiener process, or standard Brownian motion, is the continuous-time [[stochastic process|0QH5ENKZM1]] with continuous paths and independent, normally distributed increments.\nIt is the scaling limit of random walks and the basic model of random motion.\nIt is a [[Gaussian process|22WEM6RTW0]], a [[Lévy process|8NT5CFG2ZR]], a [[martingale|0D0GBNDKDH]] and a Markov process at the same time.\n\n## Explanations\n\n### L1 human\n\nPicture a pollen grain jiggling in water, or a stock price wobbling from second to second.\nThe Wiener process is the mathematical model of such motion: at every instant it moves by a small random amount, independent of the past.\nOver a time span of length $t$ it moves by a normal amount with mean $0$ and variance $t$.\nIts path is continuous but, almost surely, so rough that it has no derivative at any point.\nIf you take a fair coin-tossing walk with $n$ steps per unit of time and step size $1/\\sqrt{n}$, you get a Wiener process as $n \\to \\infty$.\n",
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