On the sequences whose conditional expectations can approximate any random variable

• Autorzy: Kaniowski K.
• Języki publikacji: EN

Abstrakty

EN

Let(Ω,F, P)be a non-atomic probability space. For a given sequence (X_n)of random variables we indicate a number of conditions whichimply that for anyrandom variable Y there exists a sequence(U_n) of σ-fields satisfying E(X_n|U_n)→Ya.s. In particular, we formulate a sufficient condition using the distributions of X_n’sonly.

Słowa kluczowe

EN

conditional expectation; almost sure convergence

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2002
• Tom: Vol. 22, Fasc. 1
• Strony: 115--126
• Opis fizyczny: Biblogr. 2 poz.

Twórcy

autor

Kaniowski K.

• Faculty of Mathematics University of Łódź, Banacha, 22,90-238 Łódź, Poland

Bibliografia

• [1] P. Billingsley, Probability and Measure, Wiley, New York, Chichester, 1979.
• [2] K. Kaniowski, On the approximation of a random variable by a conditioning of a given sequence, Probab. Math. Statist. 21 (2001), pp. 321-328.