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  "body": "\n## Summary\n\nThe Fokker–Planck equation is the parabolic equation for the probability density of a [[diffusion process|9HDQ094ADQ]].\nLet $X_t$ solve a [[stochastic differential equation|B219G9SHJA]] with drift $\\mu$ and diffusion coefficient $\\sigma$.\nThen its density $p(x, t)$ obeys a linear second-order equation built from $\\mu$ and $\\sigma\\sigma^T$.\nIts spatial operator is the adjoint of the [[infinitesimal generator|VPA41PWRR1]] of the process, which is why it is also called the forward Kolmogorov equation.\nIt links stochastic processes with partial differential equations.\n\n## Explanations\n\n### L1 human\n\nRelease many particles that drift with a velocity field and are also kicked by random noise.\nThe Fokker–Planck equation describes how the cloud of particles moves and spreads.\nThe drift term transports the density, and the noise term makes it diffuse.\nFor pure noise in one dimension, $dX = dW$, the equation is $p_t = \\frac{1}{2} p_{xx}$, a [[heat equation|VP2HN86VAG]].\n",
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