Brownian Motion: A Microscopic Dance
Understanding the Random Movement of Particles
Brownian motion, discovered by the botanist Robert Brown in 1827, is a form of random movement exhibited by microscopic particles suspended in a fluid (liquid or gas). This haphazard motion is caused by the relentless bombardment of the particle by the molecules of the surrounding fluid.
Definition of Brownian Motion
In the context of physics and biology, Brownian motion refers to the incessant and irregular zigzag movement of a particle due to its interactions with the surrounding fluid molecules. The Brownian motion is characterized by its unpredictability and lack of any discernible pattern.
Fractional Brownian Motion
Fractional Brownian motion (FBM), introduced by Kolmogorov in 1940 and rediscovered by others later on, is a variant of Brownian motion that exhibits long-range correlations in its movement patterns. FBM is used to model various phenomena in fields such as finance, hydrology, and image analysis.
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