On multiple decomposability of probability measures on R

• Autorzy: Rajba T.
• Języki publikacji: EN

Abstrakty

EN

We define multiple decomposable probability measures on R(see [18]) as a generalization of Loeve's ([6], [7]) c-decomposable laws (c G R). We consider multiply decomposability sets as a generalization of Urbanik's decomposability semigroups D(P) ([21]). We characterize Bunge's nested classes of C-decomposable laws ([1)) using the properties of multiply decomposability sets. We give representations of characteristic functions of laws, whose multiply decomposability sets contain certain sets.

Słowa kluczowe

EN

infinitely divisible measure; selfdecomposable measure

PL

defekty struktury

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 2
• Strony: 275--294
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Rajba T.

• Department of Mathematics Technical University of Łódź Branch in Bielsko-Biała ul. Willowa 2 43-309 Bielsko-Biała, Poland

Bibliografia

• [1] J. Bunge, Nested classes of C-decomposable laws, Ann. Probab. 25 (1997), 215-229.
• [2] A. Ilinskij, On c-decomposition of characteristic functions, Liet. Matem. Rink. 4 (1978), 45-50.
• [3] Z. Jurek, The classes Lm(Q) of probability measures on Banach spaces, Bull. Acad. Polon. Sci. Ser. Sci. Math. 31 (1983), 51-62.
• [4] Z. Jurek and W. Vervaat, An integral representation for selfdecomposable Banach space valued random variables, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 62 (1983), 247-262.
• [5] M. Kuczma, Functional equations in a single variable, Monografie Mat. 46, Polish Scientific Publishers (PWN), Warszawa 1968.
• [6] M. Loéve, Nouvelles classes de lois limites, Bull. Soc. Math. France 73, 1-2 (1945), 107-126.
• [7] M. Loéve, Probability Theory, New York 1955.
• [8] M. Maejima and Y. Naito (1997), Semi-selfdecomposable distributions and a new class of limit theorems, Research Report, Keio University, Japan.
• [9] F. F. Misheikis, On certain classes of limit distributions (in Russian), Litovsk. Mat. Sb. 12,4 (1972), 133-152.
• [10] F. F. Misheikis, On certain classes of limit distributions (in Russian), ibidem 12,3 (1972), 101-106.
• [11] F. F. Misheikis, On certain classes of probability laws (in Russian), ibidem 15,2 (1975), 60-65.
• [12] Nguyen van Thu, Multiply self-decomposable probability measures on Banach spaces, Studia Math. 66 (1979), 160-175.
• [13] T. Niedbalska, An example of the decomposability semigroup, Colloq. Math. 39 (1978), 137-139.
• [14] T. Niedbalska-Rajba, On decomposability semigroups on the real line, ibidem 44 (1981), 347-358.
• [15] R. P. Phelps, Lectures on Choquet's Theorem, New York 1966.
• [16] T. Rajba, On decomposability semigroups for certain probability measures, Bull. Acad. Polon. Sci. Ser. Sci. Math. 28 (1979), 415-418.
• [17] T. Rajba, A representation of distributions from certain classes LidS, Probab. Math. Statist. 4 (1984), 67-78.
• [18] T. Rajba, On certain subclasses of the classes Lc, Probab. Math. Statist. 19 (1999), 171-180.
• [19] K. Sato, Class L of multivariate distributions and its subclasses, J. Multivariate Anal. 10 (1980), 207-232.
• [20] K. Urbanik, A representation of self decomposable distributions, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 16 (1968), 209-214.
• [21] K. Urbanik, Operator semigroups associated with probability measures, ibidem 23 (1975), 75-76.
• [22] K. Urbanik, A representation of self-decomposable distributions, ibidem 16 (1968), 209-214.
• [23] K. Urbanik, Some examples of decomoposability semigroups, ibidem 24 (1976), 915-918.
• [24] K. Urbanik, Lévy's probability measures on Euclidean spaces, Studia Math. 54 (1972), 119-148.
• [25] K. Urbanik, Lévy's probability measures on Banach spaces, ibidem 63 (1987), 283-308.
• [26] O. K. Zakusilo, On classes of limit distributions in a summation scheme (in Russian), Teor. Veroyastnost. i Mat. Statist. 12 (1975), 44-48.
• [27] O. K. Zakusilo, Some properties of classes Lc of limit distributions (in Russian), ibidem 15 (1976), 68-73.