Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). This motion pattern typically consists of random fluctuations...

A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly...

fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical Brownian motion, the increments...

In science, Brownian noise, also known as Brown noise or red noise, is the type of signal noise produced by Brownian motion, hence its alternative name...

mathematical properties of the one-dimensional Brownian motion. It is often also called Brownian motion due to its historical connection with the physical...

distribution of a standard Wiener process W(t) (a mathematical model of Brownian motion) subject to the condition (when standardized) that W(T) = 0, so that...

In probability theory, reflected Brownian motion (or regulated Brownian motion, both with the acronym RBM) is a Wiener process in a space with reflecting...

In mathematics, the Dyson Brownian motion is a real-valued continuous-time stochastic process named for Freeman Dyson. Dyson studied this process in the...

thermal and statistical physics, the Brownian ratchet or Feynman–Smoluchowski ratchet is an apparent perpetual motion machine of the second kind (converting...

Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical...