On the Bernoulli two-armed bandit problem

The paper is initially concerned with monotonic properties of the posterior success probabilities when the prior success probabilities are distributed according to an arbitrary joint distribution function (Bayesian approach). Next a dynamic programming model is proposed and monotonic properties of the optimal expected cumulative discounted reward are proved. Finally, optimality properties are given for the case when one prior success probability is known.     

凸集上投影算子的一个单调性质

本文证明了投影算子的一个新的单调性质，并简要讨论了与其它单调性质的关系     

Reliability Studies of Bivariate Distributions with Pareto Conditionals

In this paper we study Arnold's (1987, Statist. Probab. Lett.5, 263–266) class of bivariate distributions with Pareto conditionals from a reliability point of view. Failure rates and mean residual life function of the marginal distributions and their monotonic properties are studied. The hazard components and their properties are investigated and their relationships with some measures of dependence are established. Finally, the failure rate of the minimum of the two components is examined and its monotonicity is investigated. Some of the results presented here are general and would be useful in studying the dependence structure in other classes of bivariate distributions.     

Monotonic time-discretized schemes in quantum control

Most of the numerical simulations in quantum (bilinear) control have used monotonically convergent algorithms of Krotov (introduced by Tannor et al. [15]), of Zhu & Rabitz [16] or their unified formulation in [17]. However, the properties of the discrete version of these procedures have not been yet tackled with. We present in this paper a stable time and space discretization which preserves the monotonic properties of the monotonic algorithms. Numerical results show that the newly derived algorithms are stable and enable various experimentations.     

The Inequality Between Two Distributions: Applications to the Analysis of Diversity Data

A new measure called diversity difference is proposed for the inequality of a pair of distributions. The diversity difference measure satisfies eight properties of a measure of inequality. This measure is simple to calculate and provides easily interpreted results.Existing inequality measures examine the distribution of a single variable whose data are arranged in a monotonic order. The new measure can employ multiple variables and does not require each to be monotonic but can be used if the data happen to be monotonic. The pair of distributions is useful for organizational diversity data because one of the distributions represents the actual proportions of employees in any class or set of classes and the other distribution is the benchmark or anchoring distribution. Data from the measure can be displayed in diversity difference trees for quick interpretation.The diversity difference measure can be arranged to define a Lorenz curve. An example with three classes (gender, race, and age) is employed to provide examples of the measure, the resulting Lorenz curve, and the disparity ratio.     

一类倒向随机微分方程L~p解对终值的单调连续性

在生成元g满足关于y单调且关于z Lipschitz连续的条件下,范(2007)得到了倒向随机微分方程L~p解对终值的单调连续结果.在g关于y单调且关于z一致连续的条件下证明了倒向随机微分方程L~p解的单调连续性,推广了范(2007)的工作,并且方法是新的.     

A certain function class related to the class of logarithmically completely monotonic functions

In this article, we introduce and investigate the notion of strongly logarithmically completely monotonic functions. Among other results, we present some properties and relationships involving this function class and several closely-related function classes.     

Inheritance of properties in communication situations

In this paper we consider cooperative games in which the possibilities for cooperation between the players are restricted because communication between the players is restricted. The bilateral communication possibilities are modeled by means of a (communication) graph. We are interested in how the communication restrictions influence the game. In particular, we investigate what conditions on the communication graph guarantee that certain appealing properties of the original game are inherited by the graph-restricted game, the game that arises once the communication restrictions are taken into account. We study inheritance of the following properties: average convexity, inclusion of the Shapley value in the core, inclusion of the Shapley values of a game and all its subgames in the corresponding cores, existence of a population monotonic allocation scheme, and the property that the extended Shapley value is a population monotonic allocation scheme. Received May 1998/Revised version January 2000     

The transformed inverse Gaussian process as an age- and state-dependent degradation model

In this paper, a transformed inverse Gaussian (TIG) process is introduced as a new family of monotonic degradation models. Different from most state-of-the-art degradation models, which can only characterize age-dependent performance degradation, the TIG process model is mainly introduced for degradation modelling of industrial products with age- and state-dependent performance degradation. With this new model, promising properties include (1) the modelling capability for characterizing products observed at discrete time points with age- and state-dependent degradation, (2) the mathematical tractability for calculating the reliability function and remaining useful life distribution with high efficiency, and (3) the modelling flexibility of incorporating explanatory variables and random effects for investigating a product population with unit-to-unit heterogeneity. To facilitate the degradation modelling and analysis, methods for parameter estimation and model selection are developed under a coherent Bayesian framework. Simulation studies and real cases are presented to demonstrate the proposed degradation model and the Bayesian methods.     

Monotonically Overrelaxed EM Algorithms

We explore the idea of overrelaxation for accelerating the expectation-maximization (EM) algorithm, focusing on preserving its simplicity and monotonic convergence properties. It is shown that in many cases, a trivial modification in the M-step results in an algorithm that maintains monotonic increase in the log-likelihood, but can have an appreciably faster convergence rate, especially when EM is very slow. The method is applicable to more general fixed point algorithms. Its simplicity and effectiveness are illustrated with several statistical problems, including probit regression, least absolute deviations regression, Poisson inverse problems, and finite mixtures. This article has supplemental materials available online.     

Testing for cointegration using induced-order statistics

In this paper we explore the usefulness of induced-order statistics in the characterization of integrated series and of cointegration relationships. We propose a non-parametric test statistic for testing the null hypothesis of two independent random walks against wide cointegrating alternatives including monotonic nonlinearities and certain types of level shifts in the cointegration relationship. We call our testing device the induced-order Kolmogorov–Smirnov cointegration test (KS), since it is constructed from the induced-order statistics of the series, and we derive its limiting distribution. This non-parametric statistic endows the test with a number of desirable properties: invariance to monotonic transformations of the series, and robustness for the presence of important parameter shifts. By Monte Carlo simulations we analyze the small sample properties of this test. Our simulation results show the robustness of the induced order cointegration test against departures from linear and constant parameter models. This paper is an extension of the work of Aparicio and Granger (1995) and Aparicio and Escribano (1998).     

Effective plastic properties of laminates

In this contribution, we make use of the fact homogenization of elastic properties of laminates [1] can be extended relatively easy to the plastic case [2] to derive exact expressions for the effective yield limit and the ultimate loading in monotonic tension test. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

集合对策中值的标准性与分配方案的单调性

本文介绍了合作对策中一种新的类型一集合对策，讨论了集合对策中三种分配方案的性质，证明了边缘贡献值和联盟力量值具有二人分配的标准性与分配方案的单调性，而共享边缘贡献值仅具有分配方案的单调性．     

A Note on the Mackey topology of a von Neumann algebra

Some of the properties of the upper bound of the spectrum of a quasilinear eigenvalue problem, subject to a positivity requirement, are derived. It is shown that, as a function of the surface heat-transfer coefficient, this parameter is a continuous, monotonic increasing function and is bounded above.     

加权累加生成的GM(1,1)模型及其应用

根据灰色系统理论中的新信息优先原理知新信息对认知的作用大于老信息的作用,而传统的累加生成没有体现原始数据中新信息的重要性.针对这一问题提出了加权累加生成的概念,并对加权累加生成在单调性、灰指数规律、凸性等方面的性质进行了研究,得到加权累加生成序列具有单调递增性,具有较强的指数规律,并具有下凸性,然后建立了基于加权累加生成的GM(1,1)模型.通过具体算例的计算表明,加权累加生成的GM(1,1)模型的模拟和预测精度比传统的GM(1,1)模型模拟和预测精度高,从而说明了该法的有效性.     

基于粒子群算法的变权累加生成的GM(1,1)模型

根据灰色系统的新信息优先原理可知新信息对认知的作用大于旧信息的作用,而传统的累加生成没有体现原始数据中新信息的重要性.针对这一问题引入了变权累加生成的方法,并对变权累加生成在单调性、灰指数规律、凸性等方面的性质进行了研究,得到变权累加生成序列具有单调递增性,具有较强的指数规律,并具有下凸性,这些性质是高精度建模的保证,然后建立了基于变权累加生成的GM(1,1)模型,并运用粒子群算法确定了变权累加生成的权重.通过具体的算例计算表明,变权累加生成的GM(1,1)模型能够提高模型的模拟和预测精度.     

Convergence analysis of a monotonic penalty method for American option pricing

This paper is devoted to study the convergence analysis of a monotonic penalty method for pricing American options. A monotonic penalty method is first proposed to solve the complementarity problem arising from the valuation of American options, which produces a nonlinear degenerated parabolic PDE with Black-Scholes operator. Based on the variational theory, the solvability and convergence properties of this penalty approach are established in a proper infinite dimensional space. Moreover, the convergence rate of the combination of two power penalty functions is obtained.     

Modified quasilinearization technique for the solution of boundary-value problems for ordinary differential equations

A new quasilinearization algorithm is presented which essentially eliminates the necessity for computer storage. The representation theorem for the standard quasilinearization procedure is reformulated in terms of the initial value of the solution to a final-value problem, leading to a modification of the successive approximations. Several theorems establishing the convergence properties are proved; as in the original procedure, these convergence properties are both quadratic and monotonic. Finally, the modified approximation scheme is illustrated through several examples.