Brownian motion - Mathematical Brownian motion

The term Brownian motion (in honor of the botanist Robert Brown) refers to either The physical phenomenon that minute particles immersed in a fluid move about randomly; or The mathematical models used to describe those random movements. The mathematical model can also be used to describe many phenomena not resembling (other than mathematically) the random movement of minute particles. An often quoted example is stock market fluctuations. Another example is the evolu ...

Including:

• Brownian motion - History
• Brownian motion - Intuitive metaphor for Brownian motion
• Brownian motion - Description of the mathematical model
• Brownian motion - Modelling the Brownian motion using differential equations
• Brownian motion - Mathematical Brownian motion
• Brownian motion - Physical Brownian motion

Read more here: » Brownian motion: Encyclopedia - Brownian motion

Jan Ingenhousz made some observations of the irregular motion of carbon dust on alcohol in 1765 but Brownian motion is generally regarded as having been discovered by the botanist Robert Brown in 1827. The story goes that Brown was studying pollen particles floating in water under the microscope. He then observed minute particles within vacuoles in the pollen grains executing the jittery motion that now bears his name. By doing the same with particles of dust, he was able to rule out that the motion was due to pollen being "alive", but it re ...

See also:

Brownian motion, Brownian motion - History, Brownian motion - Intuitive metaphor for Brownian motion, Brownian motion - Description of the mathematical model, Brownian motion - Modelling the Brownian motion using differential equations, Brownian motion - Mathematical Brownian motion, Brownian motion - Physical Brownian motion

Read more here: » Brownian motion: Encyclopedia II - Brownian motion - History

Mathematically, Brownian motion is a Wiener process in which the conditional probability distribution of the particle's position at time t + dt, given that its position at time t is p, is a normal distribution with a mean of p + μ dt and a variance of σ2 dt; the parameter μ is the drift velocity, and the parameter σ2 is the power of the noise. These properties clearly establish that Brownian motion is Markovian (i.e. it satisfies the Mark ...

See also:

Brownian motion, Brownian motion - History, Brownian motion - Intuitive metaphor for Brownian motion, Brownian motion - Description of the mathematical model, Brownian motion - Modelling the Brownian motion using differential equations, Brownian motion - Mathematical Brownian motion, Brownian motion - Physical Brownian motion

Read more here: » Brownian motion: Encyclopedia II - Brownian motion - Description of the mathematical model

The equations governing Brownian motion related slightly differently to the each of the two definitions of brownian motion given at the start of this article. Brownian motion - Mathematical Brownian motion. For a particle experiencing a brownian motion corresponding to the mathematical definition, the equation governing the time evolution of the probability density function associated to the ...

See also:

Brownian motion, Brownian motion - History, Brownian motion - Intuitive metaphor for Brownian motion, Brownian motion - Description of the mathematical model, Brownian motion - Modelling the Brownian motion using differential equations, Brownian motion - Mathematical Brownian motion, Brownian motion - Physical Brownian motion

Read more here: » Brownian motion: Encyclopedia II - Brownian motion - Modelling the Brownian motion using differential equations