Ito's Lemma (Distribution of $S_t)$

Question

If I am given that $$dS_t=S_t(\mu dt+\sigma dZ_t)$$

How do I find the distribution of $S_t$ by using Ito's Lemma? Thanks in advance.

Answer 1

As a starting point, it might be worth applying Ito's Lemma to $d(ln(S_t))$ (which should give you $(\mu −\frac{1}{2}σ^2)dt + σdW_t$).