On Certain Subclasses of the Classes Lc

• Autorzy: Rajba T.
• Języki publikacji: EN

Abstrakty

EN

Loève in [5] introduced the classes L_C associated with number c, c ϵ R, as the classes of probability measures satisfying the condition (1). Many authors investigated those classes ([2], [5]-[9], [20], [21]). In this paper we consider certain subclasses L_c1,…,_ck, L_c1(k) of the classes L_c. We prove that they coincide with the classes of distributions of series of some random variables and with the classes of limit distributions of some normed sums. We give a characterization of certain classes D_c1,…,_ck associated with L_c1,…,_ck. Urbanik in [18] introduced the concept of the decomposability semigroup associated with probability measure P, as the set of all numbers c, such that P ϵ L_C ([11]-[14]). The class L of self-decomposable distributions coincides with the class of probability measures P such that D(P) ⸧ [0, 1]. The class L_m, m ≥ 1, of multiply selfdecomposable distributions may be described as the class of probability measures P such that P ϵ L_c1,…,_cm, for every c₁,…, c_m ϵ [0, 1], or in terms of multiply decomposability semigroups it is equivalent to the inclusion D_m (P) ⸧ [0, 1]^m, where D_m (P) is the multiply decomposability semigroup defined by the formula D_m (P) = {(c₁,…, c_m); P ϵ L_c1,…,_cm} ([3], [4], [10], [15]-[17], [19]).

Słowa kluczowe

EN

subclasses; random variables; multiply selfdecomposable distributions

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1999
• Tom: Vol. 19, Fasc. 1
• Strony: 171--180
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Rajba T.

• Institute of Mathematics, Wrocław University

Bibliografia

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