Non-Recursive Base Conversion Using a Deterministic Markov Process

We prove that non-recursive base conversion can always be implemented by using a deterministic Markov process. Our paper discusses the pros and cons of recursive and non-recursive methods, in general. And we include a comparison between non-recursion and a deterministic Markov process, proving that the Markov process is twice as efficient.

Dynamics of Advantageous Mutant Spread in Spatial Death-Birth and Birth-Death Moran Models

The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized that in real-world applications, the population usually has an explicit spatial structure which can significantly influence the dynamics. In the context of cancer initiation in epithelial tissue, several recent works have analyzed the dynamics of advantageous mutant spread on integer lattices, using the biased voter model from particle systems theory. In this spatial version of the Moran model, individuals first reproduce according to their fitness and then replace a neighboring individual. From a biological standpoint, the opposite dynamics, where individuals first die and are then replaced by a neighboring individual according to its fitness, are equally relevant. Here, we investigate this death-birth analogue of the biased voter model. We construct the process mathematically, derive the associated dual process, establish bounds on the survival probability of a single mutant, and prove that the process has an asymptotic shape. We also briefly discuss alternative birth-death and death-birth dynamics, depending on how the mutant fitness advantage affects the dynamics. We show that birth-death and death-birth formulations of the biased voter model are equivalent when fitness affects the former event of each update of the model, whereas the birth-death model is fundamentally different from the death-birth model when fitness affects the latter event.

基于Markov过程天气预测的共享单车调度优化研究

针对某大学城共享单车资源分配不平衡问题,建立了与调度成本和用户满意度相关的单目标数学规划模型,对现有共享单车调度策略进行分析,并制定改善方案.通过调查问卷分析单车调度过程中存在的问题,利用Python获取单车的相关数据.在此基础上,基于齐次Markov过程对天气状况进行预测,采用LSTM时间序列对区域内未来单车数量的变化情况进行预测,利用遗传算法求解最优调度路径和调度数量,提出优化方案.通过敏感性分析验证本文所提方案的可行性.结果表明,优化后的调度方案缩短了单次调度时间并提高了用户的满意度,对共享单车管理部门具有指导意义.

具有变时滞Markov跳跃神经网络的H∞控制

文章研究了具有变时滞Markov跳跃神经网络的H∞控制。首先,设计一个输出反馈控制器,以确保Markov跳跃神经网络系统在没有外部扰动的情况下随机稳定,并在零初始条件下具有规定的干扰衰减指标。其次,利用适当的泛函和几个先进不等式获得所需控制器增益的精确数学表达式。最后,通过数值模拟的例子证明所提控制策略的有效性。

基于Markov过程的继电保护通信系统可靠性评估方法

继电保护通信系统受内外部因素影响,易出现拒动失效。传统评估方法未充分考虑动态行为、故障传播及复杂环境,导致评估结果中拒动失效率偏高。因此,文章提出基于Markov过程的继电保护通信系统可靠性评估方法。通过选取合适的可靠性评估指标全面反映系统的性能特点,利用Markov过程构建状态随机转移概率矩阵,描述系统在不同状态下的转移概率,综合评估继电保护通信系统的可靠性。实验结果表明,该方法综合考虑多种因素,拒动失效率较低,为电力系统的安全稳定运行提供有力支持。

Markov process functionals in finance and insurance

The Markov property of Markov process functionals which are frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Markov property of some important Markov process functionals are presented, the following conclusions are obtained： the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent increments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Markov process being still a Markov process are given.

Exponential stability of impulsive jump linear systems with Markov process

The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.

Modeling and Design of Real-Time Pricing Systems Based on Markov Decision Processes

A real-time pricing system of electricity is a system that charges different electricity prices for different hours of the day and for different days, and is effective for reducing the peak and flattening the load curve. In this paper, using a Markov decision process (MDP), we propose a modeling method and an optimal control method for real-time pricing systems. First, the outline of real-time pricing systems is explained. Next, a model of a set of customers is derived as a multi-agent MDP. Furthermore, the optimal control problem is formulated, and is reduced to a quadratic programming problem. Finally, a numerical simulation is presented.

数字化前后人民币汇率动态特征和路径转变分析——基于三机制Markov转换模型

通过邹氏断点检验建立人民币/美元汇率的三机制Markov转换自回归模型,选取2019年6月25日—2021年4月30日的人民币/美元汇率数据,将2020年5月29日作为人民币数字化的节点,实证分析数字人民币发展前后两个阶段的汇率机制转换特征;采用主观层次分析法计算数字人民币对当前金融体系各项指标的影响权重,分析数字人民币的发展对当前金融体系的影响程度。结果表明:数字人民币推进前,汇率在各机制上停留时间具有连续性,且均表现出高度“自维持性”;数字人民币推进后,汇率的动态转换较频繁,对外部信息冲击的反映较强烈。数字人民币进程的稳步推进对当前金融体系各方面带来不同程度的影响,对汇率的影响较明显。

SMALL PERTURBATION CRAMER METHODS AND MODERATE DEVIATIONS FOR MARKOV PROCESSES

This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviation estimations for uniformly ergodic Markov processes.

THE EQUILIBRIUM PROBLEM AND CAPACITY FOR JUMP MARKOV PROCESSES

Let X=(Omega,F,F-t,X(t),theta(t),P-x) be a jump Markov process with q-pair q(x)-q(x, A). In this paper, the equilibrium principle is established and equilibrium functions, energy, capacity and related problems is investigated in terms of the q-pair q(x)-q(x, A).

Convergence of Invariant Measures of Truncation Approximations to Markov Processes

Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Two conditions guaranteeing such convergence include exponential ergodicity and stochastic monotonicity of the process. The same also holds for processes dominated by a stochastically monotone Markov process. In addition, we shall show that finite perturbations of stochastically monotone processes may be viewed as being dominated by a stochastically monotone process, thus extending the scope of these results to a larger class of processes. Consequently, the augmentation method provides an attractive, intuitive method for approximating the stationary distributions of a large class of Markov processes on countably infinite state spaces from a finite amount of known information.

ON THE HITTING PROBABILITY AND POLARITY FOR A CLASS OF SELF-SIMILAR MARKOV PROCESSES

The anthem investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, infinity) and increasing path.

MARKOV SKELETON PROCESS IN PERT NETWORKS

In this article, we investigate Programming Evaluation and Review Technique networks with independently and generally distributed activity durations. For any path in this network, we select all the activities related to this path such that the completion time of the sub-network （only consisting of all the related activities） is equal to the completion time of this path. We use the elapsed time as the supplementary variables and model this sub-network as a Markov skeleton process, the state space is related to the subnetwork structure. Then use the backward equation to compute the distribution of the sub-network＇s completion time, which is an important rule in project management and scheduling.

Wind power time series simulation model based on typical daily output processes and Markov algorithm

The simulation of wind power time series is a key process in renewable power allocation planning,operation mode calculation,and safety assessment.Traditional single-point modeling methods discretely generate wind power at each moment;however,they ignore the daily output characteristics and are unable to consider both modeling accuracy and efficiency.To resolve this problem,a wind power time series simulation model based on typical daily output processes and Markov algorithm is proposed.First,a typical daily output process classification method based on time series similarity and modified K-means clustering algorithm is presented.Second,considering the typical daily output processes as status variables,a wind power time series simulation model based on Markov algorithm is constructed.Finally,a case is analyzed based on the measured data of a wind farm in China.The proposed model is then compared with traditional methods to verify its effectiveness and applicability.The comparison results indicate that the statistical characteristics,probability distributions,and autocorrelation characteristics of the wind power time series generated by the proposed model are better than those of the traditional methods.Moreover,modeling efficiency considerably improves.

Variance minimization for continuous-time Markov decision processes: two approaches

This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance minimization optimality equation and the existence of a variance minimal policy that is canonical, but also the existence of solutions to the two variance minimization optimality inequalities and the existence of a variance minimal policy which may not be canonical. An example is given to illustrate all of our conditions.

Digital Twin-based Quality Management Method for the Assembly Process of Aerospace Products with the Grey-Markov Model and Apriori Algorithm

The assembly process of aerospace products such as satellites and rockets has the characteristics of single-or small-batch production,a long development period,high reliability,and frequent disturbances.How to predict and avoid quality abnormalities,quickly locate their causes,and improve product assembly quality and efficiency are urgent engineering issues.As the core technology to realize the integration of virtual and physical space,digital twin(DT)technology can make full use of the low cost,high efficiency,and predictable advantages of digital space to provide a feasible solution to such problems.Hence,a quality management method for the assembly process of aerospace products based on DT is proposed.Given that traditional quality control methods for the assembly process of aerospace products are mostly post-inspection,the Grey-Markov model and T-K control chart are used with a small sample of assembly quality data to predict the value of quality data and the status of an assembly system.The Apriori algorithm is applied to mine the strong association rules related to quality data anomalies and uncontrolled assembly systems so as to solve the issue that the causes of abnormal quality are complicated and difficult to trace.The implementation of the proposed approach is described,taking the collected centroid data of an aerospace product’s cabin,one of the key quality data in the assembly process of aerospace products,as an example.A DT-based quality management system for the assembly process of aerospace products is developed,which can effectively improve the efficiency of quality management for the assembly process of aerospace products and reduce quality abnormalities.

Stability Estimation for Markov Control Processes with Discounted Cost

This article explores controllable Borel spaces, stationary, homogeneous Markov processes, discrete time with infinite horizon, with bounded cost functions and using the expected total discounted cost criterion. The problem of the estimation of stability for this type of process is set. The central objective is to obtain a bounded stability index expressed in terms of the Lévy-Prokhorov metric;likewise, sufficient conditions are provided for the existence of such inequalities.

Robust analysis of discounted Markov decision processes with uncertain transition probabilities

Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the robust range for a certain optimal policy and to obtain value intervals of exact transition probabilities.Our research yields powerful contributions for Markov decision processes(MDPs)with uncertain transition probabilities.We first propose a method for estimating unknown transition probabilities based on maximum likelihood.Since the estimation may be far from accurate,and the highest expected total reward of the MDP may be sensitive to these transition probabilities,we analyze the robustness of an optimal policy and propose an approach for robust analysis.After giving the definition of a robust optimal policy with uncertain transition probabilities represented as sets of numbers,we formulate a model to obtain the optimal policy.Finally,we define the value intervals of the exact transition probabilities and construct models to determine the lower and upper bounds.Numerical examples are given to show the practicability of our methods.

An Optimized Vertical Handoff Algorithm Based on Markov Process in Vehicle Heterogeneous Network

In order to solve the problem the existing vertical handoff algorithms of vehicle heterogeneous wireless network do not consider the diversification of network's status, an optimized vertical handoff algorithm based on markov process is proposed and discussed in this paper. This algorithm takes into account that the status transformation of available network will affect the quality of service(Qo S) of vehicle terminal's communication service. Firstly, Markov process is used to predict the transformation of wireless network's status after the decision via transition probability. Then the weights of evaluating parameters will be determined by fuzzy logic method. Finally, by comparing the total incomes of each wireless network, including handoff decision incomes, handoff execution incomes and communication service incomes after handoff, the optimal network to handoff will be selected. Simulation results show that: the algorithm proposed, compared to the existing algorithm, is able to receive a higher level of load balancing and effectively improves the average blocking rate, packet loss rate and ping-pang effect.