Let W(t) be a Brownian motion. For each of the following processes, verify whether it is a martingale process:

(1) X(t)=W^2(t)−t

(2) X(t)=W^3(t)−3tW(t)

(3) X(t)=t^2W(t)−2∫uW(u)du (The limit on the integral is 0 to t)

(4) X(t)=W^2(t)

(1) X(t)=W^2(t)−t

(2) X(t)=W^3(t)−3tW(t)

(3) X(t)=t^2W(t)−2∫uW(u)du (The limit on the integral is 0 to t)

(4) X(t)=W^2(t)

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