Toronto Math Forum
MAT4752017S => Presentations and discussions => Topic started by: kojak on April 05, 2017, 12:46:37 AM

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