Lecture 22 7 Randomness and determinism Recall the definition of the random walk: it is a discrete-time stochastic signal X = (X t) t∈Z + with the deterministic initial condition X 0 = 0 and the update rule X t+1 = X t + U t , t = 0, 1, 2,. .. and Var[X t ] = Var[U 0 +. .. + U t−1 ] = t−1 s=0 Var[U s ] = tσ 2 , where we have used the fact that U 0 ,. .. , U… (More)

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