The constant limits of sequences of defective random elements

• Autorzy: Startek M.
• Języki publikacji: EN

Abstrakty

EN

Let X, X1, X2,... be random elements. It is known, that if the sequence {Xn, n > 1} converges vaguely in probability to the random element X, then this sequence converges also vaguely to X, but not converse. In this paper it is proved, that if the limit random element X is constant, then the converse is true, i.e. if the sequence converges vaguely, then it also converges vaguely in probability. A similar dependence we have for convergences vaguely essentionaly and vaguely almost surely.

Słowa kluczowe

EN

defective measures; vague convergence; convex space

PL

przestrzeń metryczna; zbieżność błędna

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
• Rocznik: 2000
• Tom: z. 24 [181]
• Strony: 117--123
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Startek M.

• Department of Mathematics, Technical University of Rzeszów, Poland

Bibliografia

• [1] J. Kestan, K. Matthes, K., J. Mecke, Jnfinitely divisible point processes, John Wiley and Sons Ltd., New York 1978.
• [2] M. Startek, D. Szynal, On Convergence of a Sequence of Defective Random Variables, Ann. UMCS, Sec. A, Vol. L, (1996), 140-162.
• [3] D. Szynal, W. Zięba, On same Type of Convergence in Law, Bull. Acad. Pol. Sci. Ser. Math., Astr. et Phis., 22, (11), (1974), 1143-1149.