Remarks on the selfdecomposability and new examples

• Autorzy: Jurek Z.
• Języki publikacji: EN

Abstrakty

EN

The analytic property of the sel fdecomposability of characteristic functions is presented from stochastic processes point of view. This provides new examples or proofs, as well as a link between the stochastic analysis and the theory of characteristic functions. A new interpretation of the famous Levy's stochastic area formula is given.

Słowa kluczowe

EN

Levi process; Levy-Khintchine formula; Brownian motion; infinite divisibility

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 2
• Strony: 241--250
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Jurek Z.

• Institute of Mathematics University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland

Bibliografia

• 1. L. Bondesson (1992), Generalized gamma convolutions and related classes of distributions and densities, Lecture Notes in Statistics, vol. 79. Springer-Verlag, New York.
• 2. D. Dufresne (1990), The distribution of a perpetuity, with applications to risk theory and pension funding, Scand. Actuarial J., pp. 39-79.
• 3. R. K. Getoor (1979), The Brownian escape process, Ann. Probab. 7, pp. 864-867.
• 4. I. S. Gradshteyn and I. M. Ryzhik (1994), Table of integrals, series, and products, Academic Press, New York, 5th Edition.
• 5. E. Grosswald (1976), The student t-distribution of any degree of freedom is infinitely divisible, Z. Wahrsch. Verw. Gebiete vol. 36, pp. 103-109.
• 6. Z. J. Jurek (1985), Relations between the s-selfdecomposable and selfdecomposable measures, Ann. Probab. vol. 13(2), pp. 592-608.
• 7. Z. J. Jurek (1996), Series of independent exponential random variables, In: Proc. 7th Japan-Rusia Symposium on Probab. Ther. Math. Stat.; S. Watanabe, M. Fukushima, Yu.V. Prohorov, and A.N. Shiryaev Eds, pp.174-182. World Scientific, Singapore, New Jersey.
• 8. Z. J. Jurek (1997), Selfdecomposability: an exception or a rule?, Annales Univer. M. Curie-Sklodowska, Lublin-Polonia vol. LI, Sectio A, pp. 93-107. (Special volume dedicated to Professor Dominik Szynal).
• 9. Z. J. Jurek and J. D. Mason (1993), Operator limit distributions in probability theory, Wiley and Sons, New York. (292 pp.)
• 10. P. Lévy (1951), Wiener's random functions, and other Laplacian random functions; Proc. 2nd Berkeley Symposium Math. Stat. Probab., Univ. California Press, Berkeley, pp. 171-178.
• 11. K. Urbanik (1992), Functionals on transient stochastic processes with independent increments, Studia Math. vol. 103(3), pp. 299-315.
• 12. M. Wenocur (1986), Brownian motion with quadratic killing and some implications, J. Appl. Probab. 23, pp. 893-903.
• 13. M. Yor (1992), Sur certaines fonctionnelles exponentielles du mouvment Brownien reel, J. Appl. Probab. 29, pp. 202-208.
• 14. M. Yor (1992a), Some aspects of Brownian motion, Part I: Some special junctionals, Birkhauser, Basel.
• 15. M. Yor (1997), Some aspects of Brownian motion, Part II: Some recent martingale problems, Birkhauser, Basel.