We consider a stochastically continuous, affine Markov process in the sense
of Duffie, Filipovic and Schachermayer, with cadlag paths, on a general state
space D, i.e. an arbitrary Borel subset of R^d. We show that such a process is
always regular, meaning that its Fourier-Laplace transform is differentiable in
time, with derivatives that are continuous in the transform variable. As a
consequence, we show that generalized Riccati equations and Levy-Khintchine
parameters for the process can be derived, as in the case of D=R+m​×Rn studied in Duffie, Filipovic and Schachermayer (2003). Moreover, we show
that when the killing rate is zero, the affine process is a semi-martingale
with absolutely continuous characteristics up to its time of explosion. Our
results generalize the results of Keller-Ressel, Schachermayer and Teichmann
(2011) for the state space R+m​×Rn and provide a new probabilistic
approach to regularity.Comment: minor correction