@article{EJP2043,
author = {Martin Keller-Ressel and Walter Schachermayer and Josef Teichmann},
title = {Regularity of affine processes on general state spaces},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {18},
year = {2013},
keywords = {affine process, regularity, semimartingale, generalized Riccati equation},
abstract = {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 $D = R_+^m \times R^n$ 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 $R_+^m \times R^n$ and provide a new probabilistic approach to regularity.},
pages = {no. 43, 1-17},
issn = {1083-6489},
doi = {10.1214/EJP.v18-2043},
url = {http://ejp.ejpecp.org/article/view/2043}}