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Martingale Brownian Squared

Let \(W_t\) be standard Brownian Motion.

  1. Find a function  \(f(t)\) so that \(W_t^2 -f(t)\) is a Martingale.
  2. * 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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