Affine Processes on Symmetric Cones

被引：13

作者：

Cuchiero, Christa ^{[1
]}

Keller-Ressel, Martin ^{[2
]}

Mayerhofer, Eberhard ^{[3
]}

Teichmann, Josef ^{[4
]}

机构：

[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[2] Tech Univ Dresden, Inst Math Stochast, D-01062 Dresden, Germany

[3] Dublin City Univ, Dublin 9, Ireland

[4] Swiss Fed Inst Technol, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2016年 / 29卷 / 02期

关键词：

Affine processes; Symmetric cones; Non-central Wishart distribution; Wishart processes; DIFFUSIONS; MATRICES; ALGEBRA; SPACE;

D O I：

10.1007/s10959-014-0580-x

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 L,vy-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.

引用

页码：359 / 422

页数：64

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