Question: Suppose that X(t) is a Brownian motion process with mean t. a) Let Y(t) = X(t) + t, > 0. Sketch a realistic sample path

Suppose that X(t) is a Brownian motion process with mean t. a) Let Y(t) = X(t) + t, > 0. Sketch a realistic sample path (realization time series) for this process. Determine the pdf of Y (t). b) Let Z(t) = X(t) + X(t - s). Assume X(0) = 0. Determine the pdf of Z(t) for s positive.

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