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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.
Wydawca
Czasopismo
Rocznik
Tom
Strony
275--294
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
- 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.
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Bibliografia
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bwmeta1.element.baztech-article-PWA1-0038-0015