非平稳MDP--平均样本轨道最优

作者考虑的是任意状态空间，任意行动空间非平稳ＭＤＰ的平均样本轨道目标。在弱遍历条件下用鞅的极限理论，证明了最优马氏策略的存在性，推广了Ａ．Ａｒａｐｏｓｔａｔｈｉｓ，Ｖ．Ｂｏｒｋａｒ，Ｅ．Ｆ．Ｇａｕｃｈｅｒａｎｄ，Ｍ．Ｇｈｏｓｈ，Ｓ．Ｍａｒｃｕｓ（１９９３）的主要结果。     

Generalizations of the nonstationary multisplitting iterative method for symmetric positive definite linear systems

In this paper, we generalize the nonstationary parallel multisplitting iterative method for solving the symmetric positive definite linear systems. With several choices of variable weighting matrices, the convergence properties of these generalized methods can be improved. Finally, the numerical comparison of several nonstationary parallel multisplitting methods are shown.     

Maximal mean/standard deviation ratio in an undiscounted MDP

A stationary policy in an MDP (Markov decision process) induces a stationary probability distribution of the reward from each initial state. The problem analyzed here is maximization of the mean/standard deviation ratio of the stationary distribution. In the unichain case, a solution is obtained via parametric analysis of a linear program having the same number of variables and one more constraint than the formulation for gain-rate optimization. The same linear program suffices in the multichain case if the initial state is an element of choice. The easier problem of maximizing the mean/variance ratio is mentioned at the end of the paper.     

Two-Term and multi-term approximation of the nonstationary electron velocity distribution in an electric field in a gas

A very efficient, strict nonstationary multi-term approach has been developed as a generalization of the conventional and the strict nonstationary two-term approximations used for solving the nonstationary , electron Boltzmann equation. As a first application the temporal relaxation of electrons in a model plasma acted upon by a de electric field has been investigated. The results are compared with corresponding ones obtained by the conventional and the strict nonstationary two-term approach as well as with very accurate Monte Carlo simulations. Perfect agreement between nonstationary eight-term Boltzmann and Monte Carlo calculations is found.     

Analysis of nonstationary,Gaussian and non-Gaussian,generalized Langevin equations using methods of multiplicative stochastic processes

Using the methods of multiplicative stochastic processes, a thorough analysis of non-Markovian, generalized Langevin equations is presented. For the Gaussian case, these methods are used to show that the nonstationary Fokker-Planck equation already found by Adelman and others is also obtainable from van Kampen's lemma for stochastic probability flows. Here, results applicable to an arbitraryn-component process are obtained and the specific two-component case of the Brownian harmonic oscillator is presented in detail in order to explicitly exhibit the matrix algebraic methods. The non-Gaussian case is presented at the end of the paper and shows that the methods already used in the Gaussian case lead directly to results for the non-Gaussian case. In order to use the methods of multiplicative stochastic processes analysis, it is necessary to transform the non-Markovian, generalized Langevin equation using a stochastic extension of a transformation discussed by Adelman. This transformation removes the memory kernel term in the usual generalized Langevin equation and in the Gaussian case leads to the result that the original process was in fact not non-Markovian but actually nonstationary,Markovian.Supported through a fellowship from the Alfred P. Sioan Foundation.     

Borel状态空间非平稳MDP的平均方差准则

本文考虑具有 Ｂｏｒｅｌ状态空间和行动空间非平稳 ＭＤＰ的平均方差准则．首先,在遍历条件下,利用最优方程,证明了关于平均期望目标最优马氏策略的存在性．然后,通过构造新的模型,利用马氏过程的理论,进一步证明了在关于平均期望目标是最优的一类马氏策略中,存在一个马氏策略使得平均方差达到最小．作为本文的特例还得到了 Ｄｙｎｋｉｎ Ｅ． Ｂ．和 Ｙｕｓｈｋｅｖｉｃｈ Ａ． Ａ．及 Ｋｕｒａｎｏ Ｍ．等中的主要结果．     

Estimation for regression with infinite variance errors

This paper addresses the problem of modelling time series with nonstationarity from a finite number of observations. Problems encountered with the time varying parameters in regression type models led to the smoothing techniques. The smoothing methods basically rely on the finiteness of the error variance, and thus, when this requirement fails, particularly when the error distribution is heavy tailed, the existing smoothing methods due to [1], are no longer optimal. In this paper, we propose a penalized minimum dispersion method for time varying parameter estimation when a regression model generated by an infinite variance stable process with characteristic exponent α ε (1, 2). Recursive estimates are evaluated and it is shown that these estimates for a nonstationary process with normal errors is a special case.     

Combining integer programming and the randomization method to schedule employees

We describe a method to find low cost shift schedules with a time-varying service level that is always above a specified minimum. Most previous approaches used a two-step procedure: (1) determine staffing requirements and (2) find a minimum cost schedule that provides the required staffing in every period. Approximations in the first step sometimes cause the two-step approach to find infeasible or suboptimal solutions. Our method iterates between a schedule evaluator and a schedule generator. The schedule evaluator calculates transient service levels using the randomization method and identifies infeasible intervals, where the service level is lower than desired. The schedule generator solves a series of integer programs to produce improved schedules, by adding constraints for every infeasible interval, in an attempt to eliminate infeasibility without eliminating the optimal solution. We present computational results for several test problems and discuss factors that make our approach more likely to outperform previous approaches.     

Quantile forecasting and data-driven inventory management under nonstationary demand

In this paper, a single-step framework for predicting quantiles of time series is presented. Subsequently, we propose that this technique can be adopted as a data-driven approach to determine stock levels in the environment of newsvendor problem and its multi-period extension. Theoretical and empirical findings suggest that our method is effective at modeling both weakly stationary and some nonstationary time series. On both simulated and real-world datasets, the proposed approach outperforms existing statistical methods and yields good newsvendor solutions.