Stochastic partial differential equation

Summary

A stochastic partial differential equation, or SPDE, is a partial differential equation driven by random noise. Its unknown is a random field $u(t, x)$, and the noise is often space-time white noise, a random distribution that is very irregular. SPDEs extend stochastic differential equations from finitely many to infinitely many variables. They model systems with random forcing in physics, biology and finance, such as growing interfaces described by the Kardar–Parisi–Zhang equation.