I'm looking for the solution of the following SDE:
$p_{t+1} = a \cdot p_t + b + c \cdot w_t$,
where $a, b$ and $c$ are constant scalars, $w_t \sim N(0, \sigma^2)$ is a white noise and $p_t$ is discrete-time 1D stochastic process.
The solution is probably something very basic, but unfortunately I'm new to SDEs and Ito calculation. Can anyone suggest a solution?