I have good knowledge about stochastic analysis without SDE and I search for literature which explains basic definitions, existence and uniqueness results for SDEs like
$$ dX_t=\mu\left(t,X_t\right)\ dt+\sigma\left(t,X_t\right)\ dB_t. $$
with $t \in [0,T]$.
I am looking for a result that we have a unique solutions if the coefficients are locally Lipschitz with linear growth.
Does anybody know good literature for this?
I am sorry for the not precise description of the SDE, but I don't know the exact requirements.