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  "body": "\n## Summary\n\nA diffusion process is a Markov process with continuous paths, such as Brownian motion with a drift and a variable volatility.\nIts local behaviour is described by a drift vector and a diffusion matrix.\nIts [[generator|VPA41PWRR1]] is a second-order differential operator, so diffusions connect probability with parabolic and elliptic partial differential equations.\nMost diffusions are built as solutions of stochastic differential equations.\n\n## Explanations\n\n### L1 human\n\nPicture a particle of dust in a moving fluid.\nThe fluid carries it along, which is the drift.\nCollisions with molecules shake it at random, which is the diffusion part.\nThe path is continuous but very rough, like the path of Brownian motion.\nThe [[Ornstein–Uhlenbeck process|HZM2ASCDY4]], pulled back towards $0$ while being shaken, is a standard example.\n",
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