Bounds on the value of information in uncertain decision problems II†

In most stochastic decision problems one has the opportunity to collect information that would partially or totally eliminate the inherent uncertainty. One wishes to compare the cost and value of such information in terms of the decision maker's preferences to determine an optimal information gathering plan. The calculation of the value of information generally involves oneor more stochastic recourse problems as well as one or more expected value distribution problems. The difficulty and costs of obtaining solutions to these problems has led to a focus on the development of upper and lower bounds on the various subproblems that yield bounds on the value of information. In this paper we discuss published and new bounds for static problems with linear and concave preference functions for partial and perfect information. We also provide numerical examples utilizing simple production and investment problems that illustrate the calculations involved in the computation of the various bounds and provide a setting for a comparison of the bounds that yields some tentative guidelines for their use. The bounds compared are the Jensen's Inequality bound,the Conditional Jensen's Inequality bound and the Generalized Jensen and Edmundson-Madansky bounds.     

双参数变形光子相位算符与双参数变形自旋相干态

本文构造了双参数变形光子相位算符,研究了它与双参数变形自旋相干态之间的关系,得到了一些新的结果。     

On the two-parameter fractional Brownian motion and Stieltjes integrals for Hölder functions

We extend the Stieltjes integral to Hölder functions of two variables and prove an existence and uniqueness result for the corresponding deterministic ordinary differential equations and also for stochastic equations driven by a two-parameter fractional Brownian motion.     

Set-Valued Stochastic Integrals and Equations with Respect to Two-Parameter Martingales

This article is concerned with notions of set-valued stochastic integrals driven by two-parameter martingales and increasing processes. We investigate their main properties and we consider next multivalued stochastic integral equations in the plane. We establish the existence and uniqueness of solutions to such equations as well as their additional properties.     

多模双参数变形相干态

借助一个满足量子Heisenberg-Weyl代数(H-W_q,s代数)的多模算符,给出了量子代数SU(2)_q,s和SU(1,1)_q,s的k(k≥2)模实现,并构造了相应的相干态.     

双参数指数分布的可靠寿命的广义置信下限

基于双参数指数分布定数截尾数据,利用Weerahanandi给出的广义置信区间的概念,建立了可靠寿命的广义置信下限,并从理论上证明了我们给出的广义置信下限是精确的,即基于广义置信下限的区间估计的覆盖率等于要求的置信水平.广义置信下限需要通过数值方法得到,但是计算方法是简单直接的.在小样本情形下,通过对基于广义置信下限的置信区间与Engelhardt-Bain近似置信区间覆盖率的模拟比较,发现广义置信下限更令人满意.     

双参数指数分布尺度参数变化幅度的区间估计

本文将Ｓｃｈｅｃｈｔｍａｎ（１９８３）文中的方法加以修改后应用到双参数指数分布尺度参数变化幅度ρ的估计上，得到了一个保守的置信下限，并通过随机模拟证明了这个置信下限不是平凡的。     

The Convergence Rate of Fixed-Width Sequential Confidence Intervals for a Parameter of an Exponential Distribution

In this paper we consider sequential fixed-width confidence interval estimation for a parameter = aµ + b with a and b being given constants when the location parameter µ and the scale parameter of the negative exponential distribution are unknown. We investigate the rate of convergence of the coverage probability for fixed-width sequential confidence intervals of .     

A. S. Convergence of two-parameter banach space valued martingales and the radon-nikodym property of banach spaces

In this paper, we prove that under theF ₄ conditions, anyL log⁺ L bounded two-parameter Banach spece valued martingale converges almost surely to an integrable Banach space valued random variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains true if theF ₄ condition is replaced by the weaker localF ₄ condition. Project supported by the National Natural Science Foundation of China and the State Education Commission Ph. D. Station Foundation     

非线性不适定算子方程的双参数正则化方法

对非线性不适定算子方程,引入一种双参数正则化方法求解,讨论了这种正则化方法解的存在性、稳定性和收敛性.