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We consider a stochastically continuous, affine Markov process in the senseof Duffie, Filipovic and Schachermayer, with cadlag paths, on a general statespace D, i.e. an arbitrary Borel subset of R^d. We show that such a process isalways regular, meaning that its Fourier-Laplace transform is differentiable intime, with derivatives that are continuous in the transform variable. As aconsequence, we show that generalized Riccati equations and Levy-Khintchineparameters for the process can be derived, as in the case of $D = R_+^m \timesR^n$ studied in Duffie, Filipovic and Schachermayer (2003). Moreover, we showthat when the killing rate is zero, the affine process is a semi-martingalewith absolutely continuous characteristics up to its time of explosion. Ourresults generalize the results of Keller-Ressel, Schachermayer and Teichmann(2011) for the state space $R_+^m \times R^n$ and provide a new probabilisticapproach to regularity.

Regularity of affine processes on general state spaces