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Affine processes on symmetric cones. (English) Zbl 1342.60125
Summary: 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 M.-F. Bru [ibid. 4, No. 4, 725–751 (1991; Zbl 0737.60067)] and C. Cuchiero et al. [Ann. Appl. Probab. 21, No. 2, 397–463 (2011; Zbl 1219.60068)], in the more general context of symmetric cones, which also allows for simpler, alternative proofs.

##### MSC:
 60J25 Continuous-time Markov processes on general state spaces
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