An application of the Choquet theorem to the study of randomly-superinvariant measures

• Autorzy: Rajba T.
• Języki publikacji: EN

Abstrakty

EN

Given a real valued random variable Θ we consider Borel measures μ on Β (R), which satisfy the inequality μ(B) ≥ Eμ (B-Θ) (B ∈ Β (R)) or the integral inequality [formula].We apply the Choquet theorem to obtain an integral representation of measures μ satisfying this inequality. We give integral representations of these measures in the particular cases of the random variable Θ.

Słowa kluczowe

EN

backward translation operator; backward difference operator; integral inequality; extreme point

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2012
• Tom: Vol. 32, no. 2
• Strony: 317--326
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Rajba T.

• University of Bielsko-Biała Department of Mathematics and Computer Science ul. Willowa 2, 43-309 Bielsko-Biała, Poland,

Bibliografia

• [1] G. Anichini, G. Conti, Existence of solutions of some quadratic integral equations, Opuscula Math. 28 (2008) 4, 433–440.
• [2] M. Bessenyei, Zs. Páles, Characterizations of convexity via Hadamard’s inequality, Math. Inequal. Appl. 9 (2006) 1, 53–62.
• [3] M. Bessenyei, Zs. Páles, Characterization of higher-order monotonicity via integral inequalities, Proc. R. Soc. Edinburgh Sect. A 140A (2010), 723–735.
• [4] R. Kapica, J. Morawiec, Continuous solutions of iterative equations of infinite order, Opuscula Math. 29 (2009) 2, 147–155.
• [5] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Prace Naukowe Uniwersytetu Slaskiego w Katowicach, vol. 489, Panstwowe Wydawnictwo Naukowe – Uniwersytet Slaski, Warszawa-Kraków-Katowice, 1985.
• [6] M. Loéve, Nouvelles classes de lois limites, Bull. Soc. Math. France 73 (1945), 107–126.
• [7] R.P. Phelps, Lectures on Choquet’s Theorem, New York, 1966.
• [8] T. Rajba, A generalization of multiple Wright-convex functions via randomization, Preprint ATH 17 (2010).
• [9] T. Rajba, A generalization of multiply monotone functions, Radovi Matematicki 11 (2002/03), 271–293.