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.

Multiyear Discrete Stochastic Programming with a Fuzzy Semi-Markov Process

Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.

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.

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.

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.

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).

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.

MOMENTS OF PASSAGE TIMES AND ASYMPTOTIC BEHAVIOR OF INCREASING SELF-SIMILAR MARKOV PROCESSES

By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in （0, ~）. We Mso investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.

SOME CHARACTERS OF A CLASS OF ORNSTEIN-UHLENBECK TYPE MARKOV PROCESSES WITH STABLE PROCESSES

This article concerns a class of Ornstein-Uhlenbeck type Markov processes and for which the level sets will be approached. By constructing a new class f processes, we shall obtain an inequality on the Hausdorff dimensions of the level sets for the Ornstein-Uhlenbeck type Markov processes. Based on this result, we finally verify that any two independent O-U.M.P with alpha-stable processes could collide with probability one.

Seismic response evaluation of the impact of corrosion on buried pipelines based on the Markov process

Water distribution and gas supply systems are among the infrastructure systems that have many buried steel pipelines. Corrosion gradually appears inside and outside of the pipe walls over the service life of these pipelines, the corrosion is primarily caused by the surrounding soil and the materials that flow through the pipelines. However, due to the uncertainty of the characteristics of the soil and materials, the size of the corrosion region is a stochastic variable. In this paper, using a homogeneous Markov process, a model is presented to simulate the occurrence of corrosion. Then, in combinations with a linear corrosion development model, the probability density function of the pipeline area corrosion percentage is derived. Based on the corrosion model, the pipeline seismic displacements and stresses are predicted. Furthermore, using the random perturbation approach, the mean and variance of the pipeline seismic response are given. To illustrate the validity of the proposed approach, a 200-meter long pipeline is numerically investigated and its random seismic response is obtained.

FTC of hidden Markov process with application to resource allocation in air operation

This paper investigates the feedback control of hidden Markov process（HMP） in the face of loss of some observation processes.The control action facilitates or impedes some particular transitions from an inferred current state in the attempt to maximize the probability that the HMP is driven to a desirable absorbing state.This control problem is motivated by the need for judicious resource allocation to win an air operation involving two opposing forces.The effectiveness of a receding horizon control scheme based on the inferred discrete state is examined.Tolerance to loss of sensors that help determine the state of the air operation is achieved through a decentralized scheme that estimates a continuous state from measurements of linear models with additive noise.The discrete state of the HMP is identified using three well-known detection schemes.The sub-optimal control policy based on the detected state is implemented on-line in a closed-loop,where the air operation is simulated as a stochastic process with SimEvents,and the measurement process is simulated for a range of single sensor loss rates.

Calculation of railway transport capacity in an emergency based on Markov process

A method is proposed to calculate the railway transport capacity in an emergency to support the dispatching work of control centers. The effect of an emergency on section transport capacity is analyzed and the basic method to calculate the transport capacity is presented. The results show that the situation-changing process in emergency is actually a Markov process. The calculation rule is presented based on division of the time segment during which the emergency lasts. The algorithm is designed to calculate the transport capacity of each time segment. The pessimistic strategy and the fuzzy strategy are proposed to determine the computing value of the transport capacity of each time segment, to satisfy the calculating requirements in different occasions. Our study shows that the method is reasonable and practical and the method can be embedded in the train dispatching system to support the operation work in an emergency.

A New Vector Markov Process for M/G/1 Queue

In this paper, by considering the stochastic proces s of the busy period and the idle period, and introducing the unfinished work as a supplementary variable, a new vector Markov process was presented to study th e M/G/1 queue again. Through establishing and solving the density evolution equa tions, the busy-period distribution, and the stationary distributions of waitin g time and queue length were obtained. In addition, the stability condition of th is queue system was given by means of an imbedded renewal process.

Approximation of an Integral Markov Process Arising in the Approximation of Stochastic Differential Equation

We provide the derivation of a new formula for the approximation of an integral Markov process arising in the approximation of stochastic differential equations. This formula extends an existing formula derived in [1]. We have shown numerically that the leading order approximation of the differential equation with noise by solving an associated averaged problem and estimating the difference between them and the result is illustrated through some examples.

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.

Development of Optimal Maintenance Policies for Offshore Wind Turbine Gearboxes Based on the Non-homogeneous Continuous-Time Markov Process

Gearbox in offshore wind turbines is a component with the highest failure rates during operation. Analysis of gearbox repair policy that includes economic considerations is important for the effective operation of offshore wind farms. From their initial perfect working states, gearboxes degrade with time, which leads to decreased working efficiency. Thus, offshore wind turbine gearboxes can be considered to be multi-state systems with the various levels of productivity for different working states. To efficiently compute the time-dependent distribution of this multi-state system and analyze its reliability, application of the nonhomogeneous continuous-time Markov process(NHCTMP) is appropriate for this type of object. To determine the relationship between operation time and maintenance cost, many factors must be taken into account, including maintenance processes and vessel requirements. Finally, an optimal repair policy can be formulated based on this relationship.

Availability analysis of private cloud safety computer platform based on the Markov process

To ensure the correctness of train control system design and development,the ways of simulation,test and formalization were compared.According to the safe critical attribute of train control system,the characters related to system safety were propounded such as real time,hybrid,distribution(concurrence)and reactivity,and the specific formal methods associated with every character were introduced in details.The analysis and classification of the methods were done based on their mathematical basis and applications,and their advantages and disadvantages were given.Analysis result indicates that every method has determinate limitations,which is determined by the essences of model checking and theory proving.It is pointed out that the presentation of new method,the expansion of existing methods and the integration of many methods will be the development trend of formalization in train control system.

Variational Principles for Asymptotic Variance of General Markov Processes

A variational formula for the asymptotic variance of general Markov processes is obtained.As application,we get an upper bound of the mean exit time of reversible Markov processes,and some comparison theorems between the reversible and non-reversible diffusion processes.

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。