TY - JOUR
T1 - Affine Processes on Symmetric Cones
AU - Cuchiero, Christa
AU - Keller-Ressel, Martin
AU - Mayerhofer, Eberhard
AU - Teichmann, Josef
N1 - Publisher Copyright:
© 2014, Springer Science+Business Media New York.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - We consider affine Markov processes taking values in convex cones. In particular, we characterize all affine processes taking values in irreducible symmetric cones in terms of certain Lévy–Khintchine triplets. This is the natural, coordinate-free formulation of the theory of Wishart processes on positive semidefinite matrices, as put forward by Bru (J Theor Probab 4(4):725–751, 1991) and Cuchiero et al. (Ann Appl Probab 21(2):397–463, 2011), in the more general context of symmetric cones, which also allows for simpler, alternative proofs.
AB - We consider affine Markov processes taking values in convex cones. In particular, we characterize all affine processes taking values in irreducible symmetric cones in terms of certain Lévy–Khintchine triplets. This is the natural, coordinate-free formulation of the theory of Wishart processes on positive semidefinite matrices, as put forward by Bru (J Theor Probab 4(4):725–751, 1991) and Cuchiero et al. (Ann Appl Probab 21(2):397–463, 2011), in the more general context of symmetric cones, which also allows for simpler, alternative proofs.
KW - Affine processes
KW - Non-central Wishart distribution
KW - Symmetric cones
KW - Wishart processes
UR - http://www.scopus.com/inward/record.url?scp=84908140659&partnerID=8YFLogxK
U2 - 10.1007/s10959-014-0580-x
DO - 10.1007/s10959-014-0580-x
M3 - Article
AN - SCOPUS:84908140659
SN - 0894-9840
VL - 29
SP - 359
EP - 422
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 2
ER -