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  "body": "\n## Summary\n\nA stochastic partial differential equation, or SPDE, is a [[partial differential equation|GC5BDZ6QBC]] driven by random noise.\nIts unknown is a random field $u(t, x)$, and the noise is often space-time white noise, a random distribution that is very irregular.\nSPDEs extend [[stochastic differential equations|B219G9SHJA]] from finitely many to infinitely many variables.\nThey model systems with random forcing in physics, biology and finance, such as growing interfaces described by the [[Kardar–Parisi–Zhang equation|RQ196EHXKC]].\n\n## Explanations\n\n### L1 human\n\nTake the [[heat equation|VP2HN86VAG]], which describes how temperature spreads in a rod.\nNow let the rod be heated by tiny random kicks, independent at every point and every instant.\nThe temperature then becomes a random function, and the equation that governs it is an SPDE.\nBecause the kicks are so rough, the solution is rough too, and even the meaning of the equation needs care.\nIn one space dimension the solution is still a continuous function, but in two or more dimensions it is only a distribution.\n",
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