Consider the overdamped Langevin equation
$$ dX_t= -\nabla V(X_t) dt + dW_t $$
with associated FPE for its density $\rho_\cdot(\cdot):\mathbb{R}\times \mathbb{R}^d\to \mathbb{R}$
$$ \partial_t \rho_t = \text{div}(\nabla \rho_t+\rho_t\nabla V). $$
Now consider the Euler Maruyama approximation with step $\tau$
$$ X^\tau_{n+1}=X^\tau_{n}-\nabla V(X^\tau_{n})\big((n+1)\tau-n\tau\big) + W_{(n+1)\tau }-W_{n\tau} $$
and its interpolation
$$X^\tau_t=X^\tau_n~~\text{for}~t\in [n\tau,(n+1)\tau).$$
My question : is there a FPE associated to the above process?