Question: 1.8. Let {Xn}, where n = 0, 1, 2, ... , be independent and identically distributed according to the normal distribution

1.8. Let {Xn}, where n = 0, ±1, ±2, ... , be independent and identically distributed according to the normal distribution

Then the series of complex-valued r.v.'s 00 inxX 00 -inxX ~e n ~e -n xXo+ 6 . + 6 . , n=1 In n=1 -111 where i = .J=T and x is real, converges a.e. and uniformly in x. (This is Wiener's representation of the Brownian motion process.)

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