Explain the important properties of Brownian motion
Explain the important properties of Brownian motion.
Expert
The significant properties of BM are as given here:
You'll notice this 'W' in the form dW like the stochastic increment term in stochastic differential equations. This might also appear as dB or dX, various authors using various letters, and sometimes with a time subscript. Although these are all similar thing!
It's frequently easiest just to think of dW as being a random number drawn by a normal distribution along with the properties:
E[dW] = 0 and E[dW^{2}] = dt.
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