MAT475-2017S > Presentations and discussions

Brownian Motion


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.



[0] Message Index

Go to full version