Affine process
= Affine process
{title2=$\log\mathbb E_x e^{\theta X_1}=A(\theta)x+B(\theta)$}
An affine process is a time-homogeneous <Markov process> whose conditional <moment-generating function> is exponential-affine in its starting state. In discrete time one writes $\log\mathbb E_x e^{\theta X_1}=A(\theta)x+B(\theta)$ on the finite <exponential moment> domain. Continuous-time definitions allow the functions to depend also on elapsed time.