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References

  1. O. E. Barndorff-Nielsen, M. Maejima, K.I. Sato. Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations. Bernoulli 12 (2006), 1--33. Math. Review 2007c:60015
  2. O. E. Barndorff-Nielsen, V. Perez-Abreu. Matrix subordinators and related upsilon transformations. Theory Probab. Appl. 52 (2008), 1--23 Math. Review 2007k:60024
  3. O. E. Barndorff-Nielsen and S. Thorbjornsen. Classical and free infinite divisibility and LÈvy processes. Quantum independent increment processes. II, 33--159, Lecture Notes in Math. 1866, 2006, Springer, Berlin. Math. Review 2007h:60043
  4. F. Benaych-Georges. Classical and free infinitely divisible distributions and random matrices. Ann. Probab. 33 (2005), 1134--1170. Math. Review 2006e:60015
  5. H. Bercovici and V. Pata. Stable laws and domains of attraction in free probability theory. Ann. of Math. 149 (1999), 1023--1060. Math. Review 2000i:46061
  6. H. Bercovici and D. Voiculescu. Free convolution of measures with unbounded support. Indiana Univ. Math. J. 42 (1993), 733--773. Math. Review 95c:46109
  7. L. Bondesson. Generalized gamma convolutions and related classes of distributions and densities. Lecture Notes in Statist. 76, Springer, New York, 1992. Math. Review 94g:60031
  8. T. Cabanal-Duvillard, A matrix representation of the Bercovici-Pata bijection Electron. J. Probab. 10 (2005), 632--661. Math. Review 2006b:15035
  9. L. F. James, B. Roynette and M. Yor. Generalized gamma convolutions, Dirichlet means, Thorin measures, with explicit examples. arXiv:0708.3932V1 [math.PR] 29 Aug 2007. Review number not available.
  10. A. Lijoi and E. Regazzini. Means of a Dirichlet process and multiple hypergeometric functions. Ann. Probab. 32 (2004), 1469--1495. Math. Review 2005c:60098
  11. M. Maejima and K.I. Sato. The Limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions. To appear in Probab. Theory Related Fields. Review number not available.
  12. B. S. Rajput and J. Rosinski. Spectral representations of infinitely divisible processes. Probab. Theory Related Fields 82 (1989), 451--487. Math. Review 91i:60149
  13. K.I. Sato. LÈvy processes and infinitely divisible distributions, Cambridge Univ. Press, Cambridge, 1999. Math. Review 2003b:60064
  14. K.I. Sato. Additive processes and stochastic integrals. Illinois J. Math. 50 (2006), 825--851 (electronic). Math. Review 2008e:60141
  15. N. Sakuma. Characterizations of the class of free self decomposable distributions and its subclasses. To appear in Inf. Dim. Anal. Quantum Probab. Review number not available.
  16. O. Thorin. On the infinite divisibility of the Pareto distribution. Scand. Actuar. J. (1977), 31--40. Math. Review 55 #4334
  17. O. Thorin. On the infinite divisibility of the lognormal distribution. Scand. Actuar. J. (1977), 121--148. Math. Review 80m:60022
  18. O. Thorin. An extension of the notion of a generalized Γ-convolution. Scand. Actuar. J. (1978), 141--149. Math. Review 80c:60030
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