 Affine process

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.