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Abstrakty
In infinite-dimensional Banach spaces there is no complete characterization of the Lévy exponents of infinitely divisible probability measures. Here we propose a calculus on Lévy exponents that is derived from some random integrals. As a consequence we prove that each selfdecomposable measure can by factorized as another selfdecomposable measure and its background driving measure that is s-selfdecomposable. This complements a result from the paper of Iksanov, Jurek and Schreiber in the Annals of Probability (2004).
Czasopismo
Rocznik
Tom
Strony
271--280
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
- [1] A. Araujo and E. Giné, The Central Limit Theorem for Real and Banach Valued Random Variables, Wiley, New York 1980.
- [2] N. H. Bingham, L´evy processes and self-decomposability in finance, Probab. Math. Statist. 26 (2) (2006), pp. 367-378.
- [3] P. Carr, H. Geman, D. Madan and M. Yor, Pricing options on realized variance, Finance Stoch. 9 (4) (2005), pp. 453-475.
- [4] R. Cuppens, Decomposition of Multivariate Probabilities, Academic Press, New York 1975.
- [5] E. Eberlein and U. Keller, Hyperbolic distributions in finance, Bernoulli 1 (1995), pp. 281-299.
- [6] A. M. Iksanov, Z. J. Jurek and B. M. Schreiber, A new factorization property of the selfdecomposable probability measures, Ann. Probab. 32 (2) (2004), pp. 1356-1369.
- [7] Z. J. Jurek, Relations between the s-selfdecomposable and selfdecomposable measures, Ann. Probab. 13 (2) (1985), pp. 592-608.
- [8] Z. J. Jurek, The random integral representation hypothesis revisited: new classes of s-selfdecomposable laws, in: Abstract and Applied Analysis, Proc. International Conf. ICAAA, Hanoi, August 2002, World Scientific, Hongkong 2004, pp. 495-514.
- [9] Z. J. Jurek and J. D. Mason, Operator-limit Distributions in Probability Theory, Wiley, New York 1993.
- [10] Z. J. Jurek and W. Vervaat, An integral representation for selfdecomposable Banach space valued random variables, Z. Wahrscheinlichkeitstheorie verw. Gebiete 62 (1983), pp. 247-262.
- [11] Z. J. Jurek and M. Yor, Selfdecomposable laws associated with hyperbolic functions, Probab. Math. Statist. 24 (1) (2004), pp. 180-190.
- [12] K. R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York-London 1967.
- [13] G. Samorodnitsky and M. S. Taqqu, Stable Non-gaussian Random Processes, Chapman and Hall, New York 1994.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-60ac4959-dfc0-4e2c-9d10-8a0fb53dd640