On the approximation of a random variable by a conditioning of a given sequence

• Autorzy: Kaniowski K.
• Języki publikacji: EN

Abstrakty

EN

Let (Ω,F, P) be a non-atomic probability space. If (X_n) is a sequence of r.v.’s satisfying X_n → 0 a.s. (respectively, in probability) as n→∞ and EX⁺_n→∞, EX^-_n→ ∞, as n → ∞, then for any r.v. Y there exists a sequence (U_n) of σ-fields such that E(X_n|U_n|)→Ya.s. (respectively, in probability) as n→∞.

Słowa kluczowe

EN

conditional expectation; almost sure convergence; stochastic convergence

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 2
• Strony: 321--328
• Opis fizyczny: Bibliogr. 3 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 1979.
• [2] A. Paszkiewicz, On the almost, sure convergence of all conditionings of positive random variables, to appear.
• [3] A. Paszkiewicz, The. characterization of a.s. convergence of all conditionings for sequences of random vectors, to appear.