Let W be a q dimensional Brownian motion on a filtered probability space $(\Omega,\mathcal{F},\mathbb{F}=(\mathcal{F}_t)_{t \in [0,T]},\mathbb{P})$ and $x_0 \in \mathbb{R}^d$. Let $b:\mathbb{R}^d \rightarrow \mathbb{R}^{d},\sigma:\mathbb{R}^d \rightarrow \mathbb{R}^{d \times q}$ be measureable s.t. $b$ and $\sigma$ are locally Lipschitz and with linear growth.
I can not find any reference for a proof that in this case we have a unique strong solution to the SDE
$$ dX_t=b(X_t)dt+\sigma(X_t)dW_t, X_0=x_0.$$
I would be very grateful for a reference.