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  "body": "\n## Summary\n\nThe stopped process $X^\\tau$ of a [[stochastic process|0QH5ENKZM1]] $X$ at a [[stopping time|WND87FBAKC]] $\\tau$ follows $X$ up to time $\\tau$.\nAfter time $\\tau$ it stays frozen at the value $X_\\tau$.\nStopping preserves the [[martingale|0D0GBNDKDH]] property, which is the heart of the [[optional stopping theorem|DC9HZT2HVJ]].\nIt is also the basic operation of localisation, used to define [[local martingales|XC2YPC2BSW]] and stochastic integrals.\n\n## Explanations\n\n### L1 human\n\nPicture a gambler's fortune changing over time, and a rule telling the gambler when to leave the table.\nAfter leaving, the fortune no longer changes.\nThe stopped process is this frozen record: equal to the fortune until the gambler leaves, and constant afterwards.\nFor a random walk stopped when it first reaches $5$ or $-5$, the stopped walk stays between $-5$ and $5$ for ever.\n",
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