Matrix Subordinators and Related Upsilon Transformations

By Ole E. Barndorff-Nielsen, V. Pérez-Abreu. 2008

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THE MULTIVARIATE supOU STOCHASTIC VOLATILITY MODEL (2013, methodology): “For details on matrix subordinators, i.e., Lévy processes in the positive semidefinite matrices, we refer to Barndorff-Nielsen and Pérez-Abreu (2008).”
Multivariate supOU processes (2010, background): “Let us briefly recall that a d × d positive semi-definite OU-type process (see [8]) is defined as the unique càdlàg solution of the SDE d t = (A t + tA∗) dt + dLt , 0 ∈ Sd , with A ∈ Md(R) and L being a d × d matrix subordinator (see [5]), that is, a Lévy process in Sd with Lt − Ls ∈ Sd ∀s, t ∈ R+, ”
A multivariate Ornstein-Uhlenbeck type stochastic volatility model (2009, methodology): “Barndorff-Nielsen and Pérez-Abreu (2008), for example, discuss matrix subordinators which are generalizations of stable, tempered stable and Gamma subordinators.”