Let \(W_t\) be standard Brownian Motion.

- Find a function \(f(t)\) so that \(W_t^2 -f(t)\) is a Martingale.
- * Argue that in some sense this \(f(t)\)is unique among increasing functions with finite variation. Compare this with the problem here.

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Let \(W_t\) be standard Brownian Motion.

- Find a function \(f(t)\) so that \(W_t^2 -f(t)\) is a Martingale.
- * Argue that in some sense this \(f(t)\)is unique among increasing functions with finite variation. Compare this with the problem here.