Selfdecomposability perpetuity laws and stopping times

• Autorzy: Jurek Z. J.
• Języki publikacji: EN

Abstrakty

EN

The decomposability property of Lévy class L of probability distributions, on a Banach space, is extended to a family of stopping times associated with background driving Lévy processes (BDLP). As consequences, this allows us to show that all selfdecomposable measures are perpetuity laws and to get a representation of gamma distribution as an infinite product of independent uniform distributions.

Słowa kluczowe

EN

Lévy class; Banach space; selfdecomposable distributions; Lévy rocess

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1999
• Tom: Vol. 19, Fasc. 2
• Strony: 413--419
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Jurek Z. J.

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

Bibliografia

• [1] P. Billingsley, Probability and Measure, 3rd edition, Wiley, New York 1995.
• [2] D. Dufresne, On the stochastic equation ℒ (X) = ℒ [B (X + C)] and a property of gamma distributions, Bernoulli 2 (3) (1996), pp. 287-291.
• [3] P. Embrechts and Ch. M. Goldie, Perpetuities and random equation, in: Asymptotic Statistics. Proceedings of the 5th Prague Symposium, September 4-9, 1993, P. Mandl and M. Hušková (Eds.), Physica-Verlag, Heidelberg 1994, pp. 75-86.
• [4] Ch. M. Goldie and R. Grübel, Perpetuities with thin tails, Adv. in Appl. Probab. 28 (1996), pp. 463-480.
• [5] Z. J. Jurek, An integral representation of operator selfdecomposable random variables, Bull. Acad. Polon. Sci. 30 (1982), pp. 385-393.
• [6] - Series of independent exponential random variables, in: Proceedings of the Seventh Japan--Russian Symposium: Probability Theory and Mathemtical Statistics. Tokyo. July 1995, World Scientific, 1996, pp. 174-182.
• [7] - Selfdecomposability: an exception or a rule?, Ann. Univ. Mariae Curie-Skłodowska, Lublin-Polonia, Sect. A., 51 (1997), pp. 93-107.
• [8] - and J. D. Mason, Operator-limit Distributions in Probability Theory, Wiley, New York 1993.
• [9] A. N. Shiryaev, Sequential Statistical Analysis (in Russian), Nauka, Moskva 1976.