On distributions of conditional expectations

• Autorzy: Paszkiewicz A.
• Języki publikacji: EN

Abstrakty

EN

Let F and G be distribution functions on R. Then there exist a random variable X and a σ-field U satisfying P(X < a) = F(a), P(E(X|U) < a) = G(a) .[formula]. The consideration is kept on a rather elementary level.

Słowa kluczowe

EN

distribution of random variable; conditional expectation

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 2
• Strony: 287--291
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Paszkiewicz A.

• Faculty of Mathematics, University of Łódź, Banacha 22, PL-90-238 Łódź, Poland
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, PL-00-950 Warszawa, P.O. Box 137, Poland

Bibliografia

• [1] J. Jakubowski and S. Kwapie6, On multiplicative systems of functions, Bull. Acad. Polon. Sci. 27 (1979), pp. 689-694.
• [2] J. Karamata, Sur une inégalité relative aux fonctions convexes, Publ. Math. Univ. Belgrade 1 (1932), pp. 145-148.
• [3] W. Marshall and I. Olkin, Inequalities: Theory of Majorization and Its Applications, Academic Press, New York 1979.
• [4] P. A. Meyer, Probability and Potentials, Blaisdell Publishing Company, 1966.
• [5] H. V. Weizsacker and G: Winkler, Nan-compact extremal integral representations: some probabilistic aspects, in: Functional Analysis: Surveys and Recent Results 2, K.-D. Bierstedt and B. Fuchssteier(E ds.), North-Holland Publishing Company, 1980.