Results 41 to 50 of about 1,049 (74)

Maximal ϕ-inequalities for demimartingales

Journal of Inequalities and Applications, 2011
In this paper, we establish some maximal ϕ-inequalities for demimartingales that generalize the results of Wang (Stat. Probab. Lett. 66, 347-354, 2004) and Wang et al. (J. Inequal. Appl. 2010(838301), 11, 2010) and improve Doob's type inequality for
Gong Xiaobing
doaj  

The 123 theorem of Probability Theory and Copositive Matrices

Special Matrices, 2014
Alon and Yuster give for independent identically distributed real or vector valued random variablesX, Y combinatorially proved estimates of the form Prob(∥X − Y∥ ≤ b) ≤ c Prob(∥X − Y∥ ≤ a). We derivethese using copositive matrices instead.
Kovačec Alexander, Moreira Miguel M. R., Martins David P.   +2 more
doaj   +1 more source

Approximate Gaussian isoperimetry for k sets [PDF]

, 2011
Given $2\le k\le n$, the minimal $(n-1)$-dimensional Gaussian measure of the union of the boundaries of $k$ disjoint sets of equal Gaussian measure in $\R^n$ whose union is $\R^n$ is of order $\sqrt{\log k}$.
Schechtman, Gideon
core   +2 more sources

Antisymmetry of the Stochastical Order on all Ordered Topological Spaces

Analysis and Geometry in Metric Spaces, 2019
In this short note, we prove that the stochastic order of Radon probability measures on any ordered topological space is antisymmetric. This has been known before in various special cases. We give a simple and elementary proof of the general result.
Fritz Tobias
doaj   +1 more source

On the Wassertein distance for a martingale central limit theorem

, 2020
We prove an upper bound on the Wassertein distance between normalized martingales and the standard normal random variable, which extends a result of R\"ollin [Statist. Probabil. Lett. 138 (2018) 171-176]. The proof is based on a method of Bolthausen [Ann.
Fan, Xiequan, Ma, Xiaohui
core  

The Hoffmann-Jorgensen inequality in metric semigroups

, 2017
We prove a refinement of the inequality by Hoffmann-Jorgensen that is significant for three reasons. First, our result improves on the state-of-the-art even for real-valued random variables. Second, the result unifies several versions in the Banach space
Khare, Apoorva, Rajaratnam, Bala
core   +1 more source

Dependence properties of bivariate copula families

Dependence Modeling
Motivated by recently investigated results on dependence measures and robust risk models, this article provides an overview of dependence properties of many well known bivariate copula families, where the focus is on the Schur order for conditional ...
Ansari Jonathan, Rockel Marcus
doaj   +1 more source

VaR bounds in models with partial dependence information on subgroups

Dependence Modeling, 2017
We derive improved estimates for the model risk of risk portfolios when additional to the marginals some partial dependence information is available.We consider models which are split into k subgroups and consider various classes of dependence ...
Rüschendorf Ludger, Witting Julian
doaj   +1 more source

Risk bounds with additional information on functionals of the risk vector

Dependence Modeling, 2018
We consider the problem of determining risk bounds for the Value at Risk for risk vectors X where besides the marginal distributions also information on the distribution or on the expectation of some functionals Tj(X), 1 ≤ j ≤ m, is available.
Rüschendorf L.
doaj   +1 more source

An improved bound for the Gaussian concentration inequality

, 2019
In this note, we provide an improved bound for the Gaussian concentration inequality. Our proof is short and bases on the integration-by-parts formula for the gaussian measure.Comment: 4 ...
Dung, Nguyen Tien
core