Hello.... In the definition of General Random walk it is said to have stationary independent increments.......it is obvious that the increments are independent......but what does stationarity means here.......do we need to consider X(t+u)-X(t) for all t and u at the same time and try to prove that they form a stationary process or do we have to fix the length u = 1 in which case we get the dicrete white noise as a single step increments (which is stationary)
I would consider the distribution of the increments directly, as opposed to x(t+u)-x(t). They are stationary if their statistical properties do not change over time.
