Markov Stochastic Process Research Articles

Anti-disturbance fault tolerant initial alignment for inertial navigation system subjected to multiple disturbances

Modeling error, stochastic error of inertial sensor, measurement noise and environmental disturbance affect the accuracy of an inertial navigation system (INS). In addition, some unpredictable factors, such as system fault, directly affect the reliability of INSs. This paper proposes a new anti-disturbance fault tolerant alignment approach for a class of INSs subjected to multiple disturbances and system faults. Based on modeling and error analysis, stochastic error of inertial sensor, measurement noise, modeling error and environmental disturbance are formulated into different types of disturbances described by a Markov stochastic process, Gaussian noise and a norm-bounded variable, respectively. In order to improve the accuracy and reliability of an INS, an anti-disturbance fault tolerant filter is designed. Then, a mixed dissipative/guarantee cost performance is applied to attenuate the norm-bounded disturbance and to optimize the estimation error. Slack variables and dissipativeness are introduced to reduce the conservatism of the proposed approach. Finally, compared with the unscented Kalman filter (UKF), simulation results for self-alignment of an INS are provided based on experimental data. It can be shown that the proposed method has an enhanced disturbance rejection and attenuation performance with high reliability.

Jet evolution in a dense medium: event-by-event fluctuations and multi-particle correlations

We study the gluon distribution produced via successive medium-induced branchings by an energetic jet propagating through a weakly-coupled quark-gluon plasma. We show that under suitable approximations, the jet evolution is a Markovian stochastic process, which is exactly solvable. For this process, we construct exact analytic solutions for all the n-point correlation functions describing the gluon distribution in the space of energy [M. A. Escobedo, E. Iancu, Event-by-event fluctuations in the medium-induced jet evolution, JHEP 05 (2016) 008. arXiv:arXiv:1601.03629, doi:http://dx.doi.org/10.1007/JHEP05(2016)008, M. A. Escobedo, E. Iancu, Multi-particle correlations and KNO scaling in the medium-induced jet evolution, JHEP 12 (2016) 104. arXiv:arXiv:1609.06104, doi:http://dx.doi.org/10.1007/JHEP12(2016)104]. Using these results, we study the event-by-event distribution of the energy lost by the jet at large angles and of the multiplicities of the soft particles which carry this energy. We find that the event-by-event fluctuations are huge: the standard deviation in the energy loss is parametrically as large as its mean value [M. A. Escobedo, E. Iancu, Event-by-event fluctuations in the medium-induced jet evolution, JHEP 05 (2016) 008. arXiv:arXiv:1601.03629, doi:http://dx.doi.org/10.1007/JHEP05(2016)008]. This has important consequences for the phenomenology of di-jet asymmetry in Pb+Pb collisions at the LHC: it implies that the fluctuations in the branching process can contribute to the measured asymmetry on an equal footing with the geometry of the di-jet event (i.e. as the difference between the in-medium path lengths of the two jets). We compute the higher moments of the multiplicity distribution and identify a remarkable regularity known as Koba-Nielsen-Olesen (KNO) scaling [M. A. Escobedo, E. Iancu, Multi-particle correlations and KNO scaling in the medium-induced jet evolution, JHEP 12 (2016) 104. arXiv:arXiv:1609.06104, doi:http://dx.doi.org/10.1007/JHEP12(2016)104]]. These predictions could be tested via event-by-event measurements of the di-jet asymmetry.

Structure-Property Relationships of Poly(ethylene carbonate) and Poly(propylene carbonate).

Conformational characteristics of poly(ethylene carbonate) (PEC) and poly(propylene carbonate) (PPC) have been revealed via molecular orbital (MO) calculations and nuclear magnetic resonance (NMR) experiments on model compounds with the same bond sequences as those of the polycarbonates. Bond conformations derived from the MO calculations on the models were in exact agreement with those from the NMR experiments. Both PEC and PPC were indicated to adopt distorted conformations including a number of gauche bonds and cover themselves with negative charges, thus failing to form a regular packing and remaining amorphous. The MO data were applied to the refined rotational isomeric state (RIS) calculations to yield configurational properties such as the characteristic ratio, its temperature coefficient, the configurational entropy, and average geometrical parameters of unperturbed PEC and PPC chains. In the RIS calculations on PPC, the regio- and stereosequences were generated according to the Bernoulli trial or Markov stochastic process. In consequence, it was shown that the configurational properties of PPC do not depend significantly on its regio- and stereoregularities. The internal energy contribution to rubberlike chain elasticity, calculated from the temperature coefficient of the characteristic ratio, has indicated the possibility that PEC and PPC will behave as elastomers. The practical applications and potential utilizations of the polycarbonates are discussed on the basis of the conformational characteristics and configurational properties.

Estimating railway rail service life: A rail-grid-based approach

Precise estimation of railway rail service life is of great significance for the efficient use of maintenance and replacement resources and the effective prevention of broken rails. Here, an innovative model for railway rail service life estimation is proposed. A railway line is divided into adjacent segments of the same specific length. Each segment is termed a “rail grid.” Employing the theory of Markov stochastic processes and hazard models, the service life of each rail grid is estimated and the degradation law of each rail grid is customized. The proposed model is verified using five-year rail inspection data for the Longhai Railway. Our evaluation demonstrates that the estimated rail service life is very close to the real rail service life and meets railway management requirements.

Development of Neuron Ion Channel Model using Colored Noise Terms in the Conductance

The aim of this study is the ion channel model with noise variance as approximations to the Hodgkin-Huxley model proposed, due to the Hodgkin-Huxley model affected when inserting some colored noise terms inside the conductances, where those effects captured by colored noise because of the gate multiplicity. Firstly, it introduces the comparison of ion channel based on Fox, Lu and Linaro models. Additionally, in order to overcome the limitations of other parameter estimation methods, the proposed method fully constrains their models and obtains all model's capabilities of reproducing the data. Finally, the relationship between the sequence of colored noise and the spike frequency are simulated efficiently each gate compared with microscopic simulations of the stochastic Markov process method. In simulation results, the spiking rate generated from the proposed model very close to microscopic simulations and doesn’t effect by the membrane size.

The relationship between intensity and stochastic matrices for continuous-time discrete value stochastic non-homogeneous processes with Markov property

The matrices of non-homogeneous Markov processes consist of time-dependent functions whose values at time form typical intensity matrices. For solvingsome problems they must be changed into stochastic matrices. A stochas-tic matrix for non-homogeneous Markov process consists of time-dependent functions, whose values are probabilities and it depend on assumed time pe- riod. In this paper formulas for these functions are derived. Although the formula is not simple, it allows proving some theorems for Markov stochastic processes, well known for homogeneous processes, but for non-homogeneous ones the proofs of them turned out shorter.

A rate balance principle and its application to queueing models

We introduce a rate balance principle for general (not necessarily Markovian) stochastic processes. Special attention is given to processes with birth-and-death-like transitions, for which it is shown that for any state n, the rate of two consecutive transitions from $$n-1$$ to $$n+1$$ coincides with the corresponding rate from $$n+1$$ to $$n-1$$ . We demonstrate how useful this observation is by deriving well-known, as well as new, results for non-memoryless queues with state-dependent arrival and service processes. We also use the rate balance principle to derive new results for a state-dependent queue with batch arrivals, which is a model with non-birth-and-death-like transitions.

Gradual Release of Sensitive Data under Differential Privacy

We introduce the problem of releasing private data under differential privacy when the privacy level is subject to change over time. Existing work assumes that privacy level is determined by the system designer as a fixed value before private data is released. For certain applications, however, users may wish to relax the privacy level for subsequent releases of the same data after either a re-evaluation of the privacy concerns or the need for better accuracy. Specifically, given a database containing private data, we assume that a response y1 that preserves \( \epsilon _1\)-differential privacy has already been published. Then, the privacy level is relaxed to \( \epsilon _2\), with \( \epsilon _2 > \epsilon _1\), and we wish to publish a more accurate response y2 while the joint response (y1,y2) preserves \( \epsilon _2\)-differential privacy. How much accuracy is lost in the scenario of gradually releasing two responses y1 and y2 compared to the scenario of releasing a single response that is \( \epsilon _2\)-differentially private? Our
 results consider the more general case with multiple privacy level relaxations and show that there exists a composite mechanism that achieves no loss
 in accuracy.
 We consider the case in which the private data lies within Rn with an adjacency relation induced by the \( \ell _1\)-norm, and we initially focus on mechanisms that approximate identity queries. We show that the same accuracy can be achieved in the case of gradual release through a mechanism whose outputs can be described by a lazy Markov stochastic process. This stochastic process has a closed form expression and can be efficiently sampled. Moreover, our results extend beyond identity queries to a more general family of privacy-preserving mechanisms. To this end, we demonstrate the applicability of our tool to multiple scenarios including Google’s project RAPPOR, trading of private data, and controlled transmission of private data in a social network. Finally, we derive similar results for the approximated differential privacy.
 

Applicability of the Fokker-Planck equation to the description of diffusion effects on nucleation.

The nucleation of islands in a supersaturated solution of surface adatoms is considered taking into account the possibility of diffusion profile formation in the island vicinity. It is shown that the treatment of diffusion-controlled cluster growth in terms of the Fokker-Planck equation is justified only provided certain restrictions are satisfied. First of all, the standard requirement that diffusion profiles of adatoms quickly adjust themselves to the actual island sizes (adiabatic principle) can be realized only for sufficiently high island concentration. The adiabatic principle is essential for the probabilities of adatom attachment to and detachment from island edges to be independent of the adatom diffusion profile establishment kinetics, justifying the island nucleation treatment as the Markovian stochastic process. Second, it is shown that the commonly used definition of the "diffusion" coefficient in the Fokker-Planck equation in terms of adatom attachment and detachment rates is justified only provided the attachment and detachment are statistically independent, which is generally not the case for the diffusion-limited growth of islands. We suggest a particular way to define the attachment and detachment rates that allows us to satisfy this requirement as well. When applied to the problem of surface island nucleation, our treatment predicts the steady-state nucleation barrier, which coincides with the conventional thermodynamic expression, even though no thermodynamic equilibrium is assumed and the adatom diffusion is treated explicitly. The effect of adatom diffusional profiles on the nucleation rate preexponential factor is also discussed. Monte Carlo simulation is employed to analyze the applicability domain of the Fokker-Planck equation and the diffusion effect beyond it. It is demonstrated that a diffusional cloud is slowing down the nucleation process for a given monomer interaction with the nucleus edge.

Optimal execution strategy in liquidity framework

AbstractA trader wishes to execute a given number of shares of an illiquid asset. Since the asset price also depends on the trading behaviour, the trader main aim is to find the execution strategy that minimizes the related expected costs. We solve this problem in a discrete time framework, by modeling the asset price dynamic as an arithmetic random walk with drift and volatility both modeled as Markov stochastic processes. The market impact is assumed to follow a Markov process. We found the unique execution strategy minimizing the implementation shortfall when short selling is allowed. This optimal strategy is given as solution of a forward-backward system of stochastic equations depending on conditional expectations of future values of model parameters. In the opposite case, namely when short selling is prohibited, we numerically obtain the solution for the associated Bellman equation that an optimal trading strategy must satisfy.

The application of Markov's stochastic processes in risk assessment for accounting information systems

Almost all processes in the area of business management, especially those of determining reliability of the accounting-information system in business management are connected with certain risk, i.e. they are of a stochastic character, which means that every method for solving these problems must be related to the probability theory and corresponding mathematical-statistical methods. This is why it can be noted that only reliable means for determining the reliability rate of the accounting information system are corresponding mathematical-statistical methods. Having this in mind, in this paper we tried to have the problem of forming the risk rate in the area of reliability of the accounting system solved by applying methods based on stochastic processes of Markov’s type.

Wealth Inequality and Externalities from Ex Ante Skill Heterogeneity

This paper develops an incomplete markets model with state dependent (Markovian) stochastic earnings processes and ex ante skill heterogeneity corresponding to being university educated or not. Using the Wealth and Assets Survey for Great Britain, we find that the university educated group has higher average wealth, higher earnings risk but lower within group wealth inequality. Using estimates of the earnings processes for each group to calibrate the model, we find wealth inequality within and between the groups that is consistent with the data. Moreover, the predictions for overall wealth inequality are closer to the data, compared to the benchmark model with ex ante identical households. In this framework, ex ante skill heterogeneity generates a between-group pecuniary externality which in turn leads to the predicted differences in wealth inequality between the groups and works as an amplification mechanism to increase overall wealth inequality.

Sampling of realizations of the random field formed by the sum of Markov binary processes

A statistical description of the sampling and reconstruction procedure for the realizations of a random field with jumps and four possible states is given. A realization of such a field is formed by two realizations of binary Markov stochastic processes defined on two coordinate axes. The analysis of the sampling and reconstruction procedure of this field consists of two parts. In the first part, the sampling intervals are chosen based on the given probability of missing a state. In the second part, the points of state change in the realization being reconstructed are estimated, and the variances of these estimates are calculated. These variances characterize the quality of reconstruction. An example illustrating the proposed method is discussed.

Reliability and redundancy of the internal stability of reinforced soil walls

In the present study, a new methodology for reliability assessment of the internal stability of reinforced soil walls, taking into account the highly strength-redundant character of these structures, is suggested. Internal stability is probabilistically modeled as a series configuration and as an r-out-of-m configuration. Consideration of redundancy is formulated based on transitional probabilities and Markov stochastic processes. Following the suggested framework, the updated reliability of the structure, as failure propagates among the different layers of reinforcement, can be quantified. As an illustration of the developed methodology, an example of a reinforced soil wall is analyzed and results are discussed.

Four general multivariate stationary extremal Markovian processes

ABSTRACTTwo general multivariate stationary Markovian process with maximization structure (denoted by Max-AR(1) and MaxI-AR(1)) are developed respectively. Max-AR(1) is a subclass of MaxI-AR(1). The characterization of the Max-AR(1) and MaxI-AR(1) to be stationary is studied. Some properties of the two maximization processes are derived. Two more related general multivariate stochastic Markovian process with minification structure are analogously constructed (denoted by Min-AR(1) and MinI-AR(1)). Some well known maximization and minification processes are special cases of these four extermal Markovian processes. Two of them are simulated and some point estimations are provided as an illustration of the wide application of these four processes.

Equilibrium excess-of-loss reinsurance–investment strategy for a mean–variance insurer under stochastic volatility model

ABSTRACTThis article considers an optimal excess-of-loss reinsurance–investment problem for a mean–variance insurer, and aims to develop an equilibrium reinsurance–investment strategy. The surplus process is assumed to follow the classical Cramér–Lundberg model, and the insurer is allowed to purchase excess-of-loss reinsurance and invest her surplus in a risk-free asset and a risky asset. The market price of risk depends on a Markovian, affine-form and square-root stochastic factor process. Under the mean–variance criterion, equilibrium reinsurance–investment strategy and the corresponding equilibrium value function are derived by applying a game theoretic framework. Finally, numerical examples are presented to illustrate our results.

Dynamic pricing with stochastic reference effects based on a finite memory window

Inspired by the latest empirical studies, we propose a new updating model for reference prices by assuming that consumers’ memories are limited and their recall of previous prices obeys a first-order Markov stochastic process. We investigate a dynamic pricing model with stochastic reference effects and finite memory. Consistent with the exponential smoothing model, we indicate that reference effects lead to monotonic convergence of the optimal price path to an expected steady-state price. The steady-state range tends to widen as consumers become loss-averse. The results of our numerical experiments differ from findings of certain models under the assumption of stochastic recall memory of consumers. The optimal price path fluctuates consistently around the steady state instead of remaining constant. The effect of the first price on the memory window and long-term profits decreases as the length of memory window increases.

Fluctuating systems under cyclic perturbations: Relation between energy dissipation and intrinsic relaxation processes.

This study focuses on fluctuating classical systems in contact with a thermal bath, and whose configurational energetics undergoes cyclic transformations due to interaction with external perturbing agents. Under the assumptions that the configurational dynamics is a stochastic Markov process in the overdamped regime and that the nonequilibrium configurational distribution remains close to the underlying equilibrium one, we derived an analytic approximation of the average dissipated energy per cycle in the asymptotic limit (i.e., after many cycles of perturbation). The energy dissipation is then readily translated into average entropy production, per cycle, in the environment. The accuracy of the approximation was tested by comparing the outcomes with the exact values obtained by stochastic simulations of a model case: a "particle on a ring" that fluctuates in a bistable potential perturbed in two different ways. As pointed out in previous studies on the stochastic resonance phenomenon, the dependence of the average dissipation on the perturbation period may unveil the inner spectrum of the system's fluctuation rates. In this respect, the analytical approximation presented here makes it possible to unveil the connection between average dissipation, intrinsic rates and modes of fluctuation of the system at the unperturbed equilibrium, and features of the perturbation itself (namely, the period of the cycle and the projections of the energy perturbation over the system's modes). The possibilities of employing the analytical results as a guide to devising and rationalizing a sort of "spectroscopic calorimetry" experiment, and of employing them in strategies aiming to optimize the system's features on the basis of a target average dissipation, are briefly discussed.

Fatigue damage diagnostics and prognostics of composites utilizing structural health monitoring data and stochastic processes

The procedure of damage accumulation in composites, especially during fatigue loading, is a complex phenomenon of stochastic nature which depends on a number of parameters such as type and frequency of loading, stacking sequence, material properties, and so on. Toward condition-based health monitoring and decision making, the need for not only diagnostic but also prognostic tools rises and draws increasing attention in the last few years. To this direction, we model the damage evolution in composites as a doubly stochastic hidden Markov process that manifests itself via structural health monitoring observations, that is, acoustic emission data. The damage process is modeled via an extension of the classic hidden Markov models to account for nonhomogeneity, that is, age dependence in state transitions. The observations come from acoustic emission data recorded throughout fatigue testing of open-hole carbon–epoxy coupons. A procedure that utilizes multiple observation sequences from a training dataset and estimates in a maximum likelihood sense the optimal model parameters is presented and applied in unseen data via a cross-validation rationale. Diagnostics of the most likely health state determination, average degradation level, and prognostics of the remaining useful life are among the capabilities of the presented stochastic model.

Federated Architecture for Ranking the Services in Cloud Computing

Objectives: To improve Quality of Services (QoS) and ranking cloud service providers in federated cloud environment. It is also aimed to resolve various issues faced by the user and providers in cloud. Methods: In order to avoid the workload of existing cloud model and to compete with the well-known cloud service providers, customized federated cloud provider architecture was suggested. It is suggested to manage and to maintain QoS for the submitted tasks. The proposed architecture consists of external world, middle world and internal world. Each world plays vital role for customizing the request in federated environment to enhance QoS. To avoid starvation in the architecture to suggest the differentiated module and resolves the various key issues using the Stochastic Markov process model and also evaluating the cloud providers based on the quality of service requirements. Findings: Service Level Agreement (SLA) in single and federated cloud plays a vital role in enhancing Quality of Services. Single cloud service provider representation does not provide the skilled QoS, when workload becomes high. Customized federated cloud architecture reduces the drawbacks of single cloud service provider. The proposed architecture was implemented in CloudSim using Java. The simulation result of the proposed architecture proves enhanced QoS to the user and cloud service providers. The proposed federated cloud model enhances the Quality of Services by more than 18% of existing single and federated cloud model. The parameters considered for the simulation for numbers of users, providers, load factor, turnaround time and average load deviation of tasks. Applications: This architecture can be used to rank different cloud service providers and it can be trusted for any distributed cloud services with extended QoS.