The SDE for GBM is usually specified as:
$$dX(t) = X(t)[\mu dt + \sigma dW(t)]$$
If we model diffusion as stochastic, is the following still GBM?
$$dX(t) = X(t)[\mu dt + \sigma_t dW(t)]$$
$\sigma_t$ is stochastic and is driven to an independent Brownian motion.