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  "body": "\n## Summary\n\nA Feller process is a Markov process whose transition semigroup acts nicely on continuous functions that vanish at infinity.\nThe semigroup maps such functions to such functions and is continuous in time at $0$.\nThese two conditions give a version with right-continuous paths that have left limits, the strong Markov property, and an [[infinitesimal generator|VPA41PWRR1]].\nBrownian motion, [[Lévy processes|8NT5CFG2ZR]] and many [[diffusions|9HDQ094ADQ]] are Feller processes.\n\n## Explanations\n\n### L1 human\n\nA Markov process forgets its past: only the present position matters for the future.\nFor a Feller process, the future also depends continuously on the starting point.\nIf two particles start very close, their laws at a later time are close.\nAlso, after a very short time the process has barely moved in law.\nBrownian motion on the line is the main example.\n",
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