Brownian motion is among the simplest of the continuous-time [[stochastic process|stochastic (or probabilistic) processes]], and it is a [[limit (mathematics)|limit]] of both simpler and more complicated stochastic processes (see [[random walk]] and [[Donsker's theorem]]). This [[Universality (dynamical systems)|universality]] is closely related to the universality of the [[normal distribution]]. In both cases, it is often mathematical convenience rather than the accuracy of the models that motivates their use. This is because Brownian motion, whose time derivative is everywhere infinite, is an idealised approximation to actual random physical processes, which always have a finite time scale. |
Brownian motion is among the simplest of the continuous-time [[stochastic process|stochastic (or probabilistic) processes]], and it is a [[limit (mathematics)|limit]] of both simpler and more complicated stochastic processes (see [[random walk]] and [[Donsker's theorem]]). This [[Universality (dynamical systems)|universality]] is closely related to the universality of the [[normal distribution]]. In both cases, it is often mathematical convenience rather than the accuracy of the models that motivates their use. This is because Brownian motion, whose time derivative is everywhere infinite, is an idealised approximation to actual random physical processes, which always have a finite time scale. |