Itô's Lemma Applied to W²

Junior Quant · Stochastic Calculus

Apply Itô's lemma to f(t, W_t) = W_t². Is W_t² − t a martingale?

Question

Apply Itô's lemma to

f(t, W_t) = W_t^2

. Verify that

W_t^2 - t

is a martingale. What does the compensator

t

represent in terms of quadratic variation?

2 / 10