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Brownian Motion

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kojak:
Properties of Brownian Motion

Brownian Motion is defined to be the observable random motion of particles in fluids. The motion is described analytically using the Wiener Process.

There are 4 properties describing this motion:

1. B(0) = 0
2. For all time intervals  t ≥ 0 the increments B(t) are independent random variables.
3.  for all t ≥ 0 and h > 0, the increments B(t + h) − B(t) are normally
distributed with expectation zero and variance h. (meaning there is no bias towards a certain direction for any variance h)
4. The function described by the Brownian Motion is almost always continuous.



References:

http://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/McKnight.pdf

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