Author: Ushio SumitaPublisher:
ISBN:
Category :
Languages : en
Pages : 28
Book Description
Analysis of Multivariate Markov Modulated Poisson Processes
Author: Ushio SumitaDynamic and Asymptotic Analysis of Markov Modulated Poisson Processes
Author: U. SumitaContinuos-time Markov-modulated Chains In Operations Research
Author: Alexander M AndronovPublisher: World Scientific
ISBN: 9811286175
Category : Mathematics
Languages : en
Pages : 227
Book Description
Probabilistic models are widely used for description and an analysis of various processes in system reliability, risk, queuing, data communication, logistic and storage systems. The book contains various applications of the theory of continuous-time Markov-modulated processes in operation research. All analytical results are illustrated by numerical computations. Used algorithms allow overcoming computation difficulties successfully. For example, a calculation of transient probabilities of states for a continuous-time finite Markov chain uses eigenvalues and eigenvectors of the corresponding matrix (generator). In a more complex case of differential or integral equations, such a simple explicit form of a solution is missing. The explicit form of solution is presented by means of infinity sums of functions. For example, often we have to deal with the so-called renewal equation. Its solution is presented as an infinite sum of the renewal function. In this case, an approximation of functions of interest and iterative computation procedures are used.
A Statistical Procedure for Fitting Markov-Modulated Poisson Processes
Author: Kathleen S. MeierPublisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 274
Book Description
Modelling and Understanding Count Processes Through a Markov-Modulated Non-Homogeneous Poisson Process Framework
Author: Benjamin AvanziPublisher:
ISBN:
Category :
Languages : en
Pages : 27
Book Description
The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through the introduction of a flexible frequency perturbation measure. This contribution enables known information of observed event arrivals to be naturally incorporated in a tractable manner, while the hidden Markov chain captures the effect of unobservable drivers of the data. In addition to increases in accuracy and interpretability, this method supplements analysis of the latent factors. Further, this procedure naturally incorporates data features such as over-dispersion and autocorrelation. Additional insights can be generated to assist analysis, including a procedure for iterative model improvement. Implementation difficulties are also addressed with a focus on dealing with large data sets, where latent models are especially advantageous due the large number of observations facilitating identification of hidden factors. Namely, computational issues such as numerical underflow and high processing cost arise in this context and in this paper, we produce procedures to overcome these problems. This modelling framework is demonstrated using a large insurance data set to illustrate theoretical, practical and computational contributions and an empirical comparison to other count models highlight the advantages of the proposed approach.
Markov-Modulated Processes and Semiregenerative Phenomena
Author: Loon Ching TangPublisher: World Scientific
ISBN: 9812793194
Category : Mathematics
Languages : en
Pages : 237
Book Description
The book presents a coherent treatment of Markov random walks and Markov additive processes together with their applications. Part I provides the foundations of these stochastic processes underpinned by a solid theoretical framework based on Semiregenerative phenomena. Part II presents some applications to queueing and storage systems.
A Statistical Procedure for Fitting Markov-modulated Poisson Processes
Author: Kathleen Susan MeierPublisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 246
Book Description
Renewal Characterization of Markov Modulated Poisson Processes
Author: M. F. NeutsApplications of Discrete-time Markov Chains and Poisson Processes to Air Pollution Modeling and Studies
Author: Eliane Regina RodriguesPublisher: Springer Science & Business Media
ISBN: 1461446457
Category : Mathematics
Languages : en
Pages : 116
Book Description
In this brief we consider some stochastic models that may be used to study problems related to environmental matters, in particular, air pollution. The impact of exposure to air pollutants on people's health is a very clear and well documented subject. Therefore, it is very important to obtain ways to predict or explain the behaviour of pollutants in general. Depending on the type of question that one is interested in answering, there are several of ways studying that problem. Among them we may quote, analysis of the time series of the pollutants' measurements, analysis of the information obtained directly from the data, for instance, daily, weekly or monthly averages and standard deviations. Another way to study the behaviour of pollutants in general is through mathematical models. In the mathematical framework we may have for instance deterministic or stochastic models. The type of models that we are going to consider in this brief are the stochastic ones.
Author: Anders Tolver Jensen