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Powers of Brownian motion · Part 3 of 4

$W_t$ is a standard Brownian motion started at $W_0 = 0$ . Each part asks about a function of it.

Itô’s lemma gives $d(W_t^3) = 3W_t^2\,dW_t + 3W_t\,dt$ . Which process is a martingale?

A $W_t^3$ itself, because $\mathbb{E}[W_t^3] = 0$ for every $t$
B $W_t^3 - 3tW_t$
C $W_t^3 - 3t$
D $W_t^3 - t^3$

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Itô’s lemma and the computations you will be asked for

Itô’s lemma gives d(Wt3)=3Wt2 dWt+3Wt dtd(W_t^3) = 3W_t^2\,dW_t + 3W_t\,dtd(Wt3​)=3Wt2​dWt​+3Wt​dt. Which process is a martingale?

More stochastic calculus questions

Itô’s lemma gives $d(W_t^3) = 3W_t^2\,dW_t + 3W_t\,dt$ . Which process is a martingale?