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.