Core rules

In Ito calculus, the formal rules are

$$ (dB_t)^2=dt, \qquad (dt)^2=0, \qquad dt\,dB_t=0. $$

Use

If

$$ dZ_t=X_t\,dt+Y_t\,dB_t, $$

then

$$ (dZ_t)^2

(X_t,dt+Y_t,dB_t)^2

Y_t^2,dt. $$

Why this is useful

These rules summarize the mechanics behind Ito formula, quadratic variation, and product expansions.