Remarks on the selfdecomposability and new examples

Demonstratio Mathematica

Volumn 34, Issue 2, 2001, Pages 241-250

  Jurek, Zbigniew J ^a  

^a UNIVERSITY OF WROC AW   (Poland)

Author keywords

Brownian motion; Infinite divisibility; Levy process; Levy Khintchine formula; Or SD distributions; Scaling and strong Markov property; Selfdecomposability property or class L distributions

Indexed keywords

EID: 0002276217     PISSN: 04201213     EISSN: 23914661     Source Type: Journal    
DOI: 10.1515/dema-2001-0203     Document Type: Article

References (15)

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. Dufresn e (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. Jure k (1985), Relations between the s-selfdecomposable and selfdecomposable measures, Ann. Probab. Vol. 13(2), pp. 592-608.
7. Z. J. Jure k 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, 174-182. World Scientific, Singapore, New Jersey
8. Z. J. Jure k (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. Jure k 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.