Affine Processes on Symmetric Cones |
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Authors: | Christa Cuchiero Martin Keller-Ressel Eberhard Mayerhofer Josef Teichmann |
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Institution: | 1.Faculty of Mathematics,University of Vienna,Wien,Austria;2.TU Dresden, Institut für Mathematische Stochastik,Dresden,Germany;3.Dublin City University,Dublin 9,Ireland;4.Departement Mathematik,ETH Zürich,Zurich,Switzerland |
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Abstract: | 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. |
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