Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations

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On the distribution of the Rosenblatt process (2013, methodology): “This class was extended to R by Barndorff-Nielsen et al. (2006) as follows: call Γx an elementary gamma random variable in R if x is a non-random non-zero vector in R and Γ is a gamma random variable on R+.”
Tempering stable processes (2007, background): “Accordingly to Theorem 33.1 in [22], P0|Ft and P|Ft are mutually absolutely continuous for every t > 0 if and only if (4.7) ∫ Rd ( eφ(x)/2 − 1 )2 M0(dx) ∞ and (4.8) Bα = 0.”
Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes (2012, methodology): “To also cover this and related choices, we employ the polar decomposition for Lévy measures [2], Lemma 2.”
STOCHASTIC INTEGRALS WITH RESPECT TO L´ EVY PROCESSES AND INFINITELY DIVISIBLE DISTRIBUTIONS (2011, background): “The foregoing theorems in this subsection were proved by [2, 49].”
Additive processes and stochastic integrals (2006, background): “Distributions of some improper stochastic integrals related to Thorin and Goldie–Steutel–Bondesson classes are studied in [1].”