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  "body": "\n## Summary\n\nAn excessive function of a Markov process is a nonnegative function that decreases on average along the paths of the process.\nIt is also recovered as the limit of its averages at small times.\nExcessive functions are the probabilistic counterpart of nonnegative superharmonic functions.\nFor Brownian motion the two classes coincide.\nFor general Markov processes, excessive functions play the role of superharmonic functions in an abstract potential theory.\n\n## Explanations\n\n### L1 human\n\nImagine a quantity attached to each position, and a particle moving at random.\nThe function is excessive if its expected value at the particle's later position never exceeds its value at the starting position.\nConstants are excessive, and so is the expected total time that the particle will spend in a given region.\nFor Brownian motion in space, $1/\\abs{x}$ is excessive, matching the fact that it is superharmonic.\n",
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