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  "body": "\n## Summary\n\nA stopping time is a random time $\\tau$ with the following property.\nAt each time $t$, one can decide whether $\\tau$ has already happened using only the information available at time $t$.\nFirst hitting times of sets by adapted processes are the main examples.\nStopping times are central in martingale theory, through the [[optional stopping theorem|DC9HZT2HVJ]], and in the strong Markov property and optimal stopping.\n\n## Explanations\n\n### L1 human\n\nA stopping time is a rule for when to stop that never needs to look into the future.\n\"Stop the first time the coin shows heads\" is such a rule: when it happens, you know it.\n\"Stop at the last head before the hundredth toss\" is not, because you cannot know that a head is the last one until later.\nFor a random walk started at $0$, the first time it reaches $5$ is a stopping time.\n",
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