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Show W^2 - t is a martingale
Am aware this is basic but i can't get rid of the dt term using ito's lemma though i can see it can be shown using the properties of a martingale I am confusing something and would appreciate it if someone can walk me through it.X = W^2 - tdX = (2WdW + dt) - dt....How can i show there is no drift by using: f'*dx +1/2 f''*(dx)^2thanks
Show W^2 - t is a martingale
Hello, unless I misunderstand you you've answered your own question..your stochastic process - Wfunction of W and t - X(W, t) = W^2 - tUse Ito's Lemma - dX = (2WdW + 1/2 * 2 * dw^2) - 1 dt = 2WdW + dt - dt = 2WdWYou've found that X is a process whose increments have zero drift term i.e. a martingale. HTH,Marc