[PDF] Top 20 Maximal Inequalities for Dependent Random Variables and Applications

... variables satisfying 1.1. A sufficient condition will be given under which 1.2 and 1.3 hold. We first state and prove one of our main results. The proof is based on the well known method of subsequences. Our proof ... See full document

... Since the conception of PND sequences contains independent and negatively associated sequences, which have a lot of applications, e.g. in reliability theory, Percolation theory and multivariate statistical ... See full document

... The paper is organized as follows. In Section 2 we state the MDP for weakly dependent random variables with applications to functions of mixing sequences, Markov chains, and functions of ... See full document

... WOD random variables were introduced by Wang and Cheng [] for risk ...dom variables. On the other hand, for the limit theories and applications of WOD se- quences, we refer to Shen [] for ... See full document

... Remark. Associated random variables were introduced by Esary et al. [4] and have been found many applications especially in reliability theory. Proposition 2 of Newman and Wright [3] shows that the ... See full document

... Romano and Siegel [[8], Section 4.30]) provides an example of two random variables X and Y such that the density of their sum is the convolution of their densities, yet they are not independent. It is easy ... See full document

... some inequalities for LNQD random variables, we investigate the uniformly asymptotic nor- mality of the sample quantiles for a LNQD sequence under mild conditions and obtain the rate of normal ... See full document

... PAC-Bayesian inequalities for some ran- dom variable ...symmetric random variables and the locally square integrable ...the random variable sequence, without any other dependent condi- ... See full document

... The definition of PND is given by Lehmann 2. The concept of ND is given by Bozorgnia et al. 3, and the definition of NA is introduced by Joag-Dev and Proschan 4. These conceptions of dependence random ... See full document

... new applications of fractional calculus for continuous random variables are ...weighted random variable inequalities are generated and some classical results are deduced as special ... See full document

... for some p > J F + and any δ > . Comparing with this condition, (.) is weaker due to Lemma . of Ng et al. []. The condition (.) is also satisfied for, e.g., the renewal counting process generated by ... See full document

... integral inequalities play a fundamental role in the theory of differential equations and applied ...type inequalities is also of great ...integral inequalities for the expectation E(X) and the ... See full document

... { X n , n ≥ 1 } is a sequence of ND subgaussian random variables. Since some proofs are the same as Mikosch [7], we abbreviate them. In fact we obtain upper bounds that are greater than upper bounds in ... See full document

... a random experiment is called a random variable or simply a ...dom variables are usually denoted by capital letters X, Y and Z, while the values associated to them by corresponding small letters x, y ... See full document

... independent random variables such as Taylor [13], Hu et ...negatively dependent and negatively associated random variables namely Liang and Su [10], Liang [9], Huang and Xu [5] and ... See full document

... exponential inequalities for positively associated random variables without the boundedness ...These inequalities improve the corresponding results obtained by Oliveira ...the ... See full document

... tant role in various proofs of limit theorems. In particular, it provides a measure of con- vergence rate for the strong law of large numbers. The main purpose of the paper is to present some probability ... See full document

... = ∑ X n = S n ( ) / n . Landers and Rogge [8] proved a strong law of large numbers (SLLN) for pairwise independent and strongly uniformly integrable r.v.’s. Chandra and Goswami [3] proved a more general SLLN for pairwise ... See full document

... In 1996, Isac and Rassias 30 were the first to provide applications of stability theory of functional equations for the proof of new fixed point theorems with applications. The stability problems of several ... See full document

... The purpose of the present paper is to establish some new nonlinear retarded integral inequalities of Gronwall-Bellman type with two variables. We can demonstrate that inequalities 1.4, 1.5, and 1.7, ... See full document