TAILIEUCHUNG - Conditional expectation type operators and modular inequalities

In this paper we discuss the connection between conditional expectation type operators and integral operators. A variant of Schur’s lemma is established and we obtain modular inequalities for a class of conditional expectation type operators. | Turk J Math (2018) 42: 3117 – 3122 © TÜBİTAK doi: Turkish Journal of Mathematics Research Article Conditional expectation type operators and modular inequalities Dah-Chin LUOR∗, Department of Financial and Computational Mathematics, I-Shou University, Dashu District, Kaohsiung City, Taiwan Received: • Accepted/Published Online: • Final Version: Abstract: In this paper we discuss the connection between conditional expectation type operators and integral operators. A variant of Schur’s lemma is established and we obtain modular inequalities for a class of conditional expectation type operators. Key words: Conditional expectation, modular inequalities, norm inequalities 1. Introduction Let (Ω, S, P) be a probability space and let X be a real-valued random variable on Ω . The expectation ∫ EX of X is defined as Ω XdP if the integral exists. Let A be a sub- σ -algebra of S . The conditional expectation of X given A is defined as a random variable E(X

• Toán học
• Conditional expectation
• Modular inequalities
• Norm inequalities
• Type operators
• Schur’s lemma
• Generalized Expectation Criteria
• Semi Supervised Learning
• Conditional Random Fields
• báo cáo khoa học
• báo cáo ngôn ngữ
• xử lý ngôn ngữ tự nhiên