Hi Raj, it's been over a year and half since I sat CT4 but here goes:
The independent property of a random walk just means that any two non-overlapping time periods are independent!
So for example, X_t to X_t-1 is independent of any t greater than or equal to one. (This is just maths speak. So X_4 to X_5 is independent of X_5 to X_6 etc)
The stationary property of a random walk just means that it does not depend on time, i.e. it is constant. (Formally, I vaguely remember the notes saying that the mean is constant and the covariance depends on the lag) So,
If we are told that the increment of a random walk is normally distributed with mean mu and variance sigma squared then this distribution is the same for ALL increments (Hope that helps).
Does anyone disagree?
Good luck!!
Last edited: Jan 16, 2010