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**Presentations and discussions / Brownian Motion**

« **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

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

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