Affine autoregressive process ($X_t=a{X}_{t-1}+b+{\xi }_t$)

An autoregressive process of order one with independent and identically distributed random variables as innovations is an affine process when the innovation exponential moments are finite. Its one-step coefficients are $A(\theta )=a\theta$ and $B(\theta )=b\theta +\psi (\theta )$, where $\psi$ is the innovation cumulant-generating function.