Joint affine transform

For a scalar discrete-time affine process, the conditional cumulant-generating function of ${\sum }_{j=1}^t{\theta }_j{X}_j$ is affine in $X_0$. Backward effective parameters $q_t={\theta }_t$, $q_j={\theta }_j+A(q_{j+1})$ give coefficients $A(q_1)$ and ${\sum }_{j}B(q_j)$.