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  "body": "\n## Summary\n\nA filtration is an increasing family $(\\mathcal{F}_t)_{t \\in T}$ of sub-$\\sigma$-algebras of the $\\sigma$-algebra of a probability space, indexed by time.\nThe $\\sigma$-algebra $\\mathcal{F}_t$ models the information available at time $t$, and information is never lost as time goes on.\nFiltrations are the setting for [[adapted processes|YRNFE016FF]], [[stopping times|WND87FBAKC]] and [[martingales|0D0GBNDKDH]].\n\n## Explanations\n\n### L1 human\n\nImagine watching a game of chance round by round.\nAfter each round you know more than before: all earlier results and the new one.\nA filtration records this growing knowledge: at each time it lists the events whose occurrence you can already decide.\nFor repeated coin tosses, the information at time $n$ consists of the events that depend only on the first $n$ tosses.\n",
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