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Author: Vladimir S. Korolyuk
Publisher: Springer Science & Business Media
ISBN: 940114625X
Category : Mathematics
Languages : en
Pages : 195
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Book Description
In this monograph stochastic models of systems analysis are discussed. It covers many aspects and different stages from the construction of mathematical models of real systems, through mathematical analysis of models based on simplification methods, to the interpretation of real stochastic systems. The stochastic models described here share the property that their evolutionary aspects develop under the influence of random factors. It has been assumed that the evolution takes place in a random medium, i.e. unilateral interaction between the system and the medium. As only Markovian models of random medium are considered in this book, the stochastic models described here are determined by two processes, a switching process describing the evolution of the systems and a switching process describing the changes of the random medium. Audience: This book will be of interest to postgraduate students and researchers whose work involves probability theory, stochastic processes, mathematical systems theory, ordinary differential equations, operator theory, or mathematical modelling and industrial mathematics.
Author: Vladimir S. Korolyuk
Publisher: Springer Science & Business Media
ISBN: 940114625X
Category : Mathematics
Languages : en
Pages : 195
Get Book Here
Book Description
In this monograph stochastic models of systems analysis are discussed. It covers many aspects and different stages from the construction of mathematical models of real systems, through mathematical analysis of models based on simplification methods, to the interpretation of real stochastic systems. The stochastic models described here share the property that their evolutionary aspects develop under the influence of random factors. It has been assumed that the evolution takes place in a random medium, i.e. unilateral interaction between the system and the medium. As only Markovian models of random medium are considered in this book, the stochastic models described here are determined by two processes, a switching process describing the evolution of the systems and a switching process describing the changes of the random medium. Audience: This book will be of interest to postgraduate students and researchers whose work involves probability theory, stochastic processes, mathematical systems theory, ordinary differential equations, operator theory, or mathematical modelling and industrial mathematics.
Author: Vladimir Anisimov
Publisher: John Wiley & Sons
ISBN: 1118623487
Category : Mathematics
Languages : en
Pages : 268
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Book Description
Switching processes, invented by the author in 1977, is the main tool used in the investigation of traffic problems from automotive to telecommunications. The title provides a new approach to low traffic problems based on the analysis of flows of rare events and queuing models. In the case of fast switching, averaging principle and diffusion approximation results are proved and applied to the investigation of transient phenomena for wide classes of overloading queuing networks. The book is devoted to developing the asymptotic theory for the class of switching queuing models which covers models in a Markov or semi-Markov environment, models under the influence of flows of external or internal perturbations, unreliable and hierarchic networks, etc.
Author: Alexei Kulik
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110458713
Category : Mathematics
Languages : en
Pages : 316
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Book Description
The general topic of this book is the ergodic behavior of Markov processes. A detailed introduction to methods for proving ergodicity and upper bounds for ergodic rates is presented in the first part of the book, with the focus put on weak ergodic rates, typical for Markov systems with complicated structure. The second part is devoted to the application of these methods to limit theorems for functionals of Markov processes. The book is aimed at a wide audience with a background in probability and measure theory. Some knowledge of stochastic processes and stochastic differential equations helps in a deeper understanding of specific examples. Contents Part I: Ergodic Rates for Markov Chains and Processes Markov Chains with Discrete State Spaces General Markov Chains: Ergodicity in Total Variation MarkovProcesseswithContinuousTime Weak Ergodic Rates Part II: Limit Theorems The Law of Large Numbers and the Central Limit Theorem Functional Limit Theorems
Author: Kulik, Alexei
Publisher: Universitätsverlag Potsdam
ISBN: 3869563389
Category : Mathematics
Languages : en
Pages : 138
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Book Description
The present lecture notes aim for an introduction to the ergodic behaviour of Markov Processes and addresses graduate students, post-graduate students and interested readers. Different tools and methods for the study of upper bounds on uniform and weak ergodic rates of Markov Processes are introduced. These techniques are then applied to study limit theorems for functionals of Markov processes. This lecture course originates in two mini courses held at University of Potsdam, Technical University of Berlin and Humboldt University in spring 2013 and Ritsumameikan University in summer 2013. Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.
Author: Yaroslav Chabanyuk
Publisher: John Wiley & Sons
ISBN: 1786305569
Category : Mathematics
Languages : en
Pages : 240
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Book Description
This book analyzes stochastic evolutionary models under the impulse of diffusion, as well as Markov and semi-Markov switches. Models are investigated under the conditions of classical and non-classical (Levy and Poisson) approximations in addition to jumping stochastic approximations and continuous optimization procedures. Among other asymptotic properties, particular attention is given to weak convergence, dissipativity, stability and the control of processes and their generators. Weak convergence of stochastic processes is usually proved by verifying two conditions: the tightness of the distributions of the converging processes, which ensures the existence of a converging subsequence, and the uniqueness of the weak limit. Achieving the limit can be done on the semigroups that correspond to the converging process as well as on appropriate generators. While this provides the convergence of generators, a natural question arises concerning the uniqueness of a limit semigroup.
Author: Jacques Janssen
Publisher: Springer Science & Business Media
ISBN: 0387707301
Category : Mathematics
Languages : en
Pages : 441
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Book Description
Everyone working in related fields from applied mathematicians to statisticians to actuaries and operations researchers will find this a brilliantly useful practical text. The book presents applications of semi-Markov processes in finance, insurance and reliability, using real-life problems as examples. After a presentation of the main probabilistic tools necessary for understanding of the book, the authors show how to apply semi-Markov processes in finance, starting from the axiomatic definition and continuing eventually to the most advanced financial tools.
Author: Franciszek Grabski
Publisher: Elsevier
ISBN: 0128006595
Category : Mathematics
Languages : en
Pages : 270
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Book Description
Semi-Markov Processes: Applications in System Reliability and Maintenance is a modern view of discrete state space and continuous time semi-Markov processes and their applications in reliability and maintenance. The book explains how to construct semi-Markov models and discusses the different reliability parameters and characteristics that can be obtained from those models. The book is a useful resource for mathematicians, engineering practitioners, and PhD and MSc students who want to understand the basic concepts and results of semi-Markov process theory. - Clearly defines the properties and theorems from discrete state Semi-Markov Process (SMP) theory - Describes the method behind constructing Semi-Markov (SM) models and SM decision models in the field of reliability and maintenance - Provides numerous individual versions of SM models, including the most recent and their impact on system reliability and maintenance
Author: Andrey Ronzhin
Publisher: Springer Nature
ISBN: 981155580X
Category : Technology & Engineering
Languages : en
Pages : 553
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Book Description
This book features selected papers presented at the 15th International Conference on Electromechanics and Robotics “Zavalishin's Readings” – ER(ZR) 2020, held in Ufa, Russia, on 15–18 April 2020. The contributions, written by professionals, researchers and students, cover topics in the field of automatic control systems, electromechanics, electric power engineering and electrical engineering, mechatronics, robotics, automation and vibration technologies. The Zavalishin's Readings conference was established as a tribute to the memory of Dmitry Aleksandrovich Zavalishin (1900–1968) – a Russian scientist, corresponding member of the USSR Academy of Sciences and founder of the school of valve energy converters based on electric machines and valve converters energy. The first conference was organized by the Institute of Innovative Technologies in Electromechanics and Robotics at the Saint Petersburg State University of Aerospace Instrumentation in 2006.
Author: G. George Yin
Publisher: Springer Science & Business Media
ISBN: 1461443466
Category : Mathematics
Languages : en
Pages : 442
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Book Description
This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted to applications in controlled dynamic systems, production planning, and numerical methods for controlled Markovian systems with large-scale and complex structures in the real-world problems. This second edition has been updated throughout and includes two new chapters on asymptotic expansions of solutions for backward equations and hybrid LQG problems. The chapters on analytic and probabilistic properties of two-time-scale Markov chains have been almost completely rewritten and the notation has been streamlined and simplified. This book is written for applied mathematicians, engineers, operations researchers, and applied scientists. Selected material from the book can also be used for a one semester advanced graduate-level course in applied probability and stochastic processes.
Author: Dmitri Koroliouk
Publisher: John Wiley & Sons
ISBN: 1786309114
Category : Mathematics
Languages : en
Pages : 276
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Book Description
This book illustrates a number of asymptotic and analytic approaches applied for the study of random evolutionary systems, and considers typical problems for specific examples. In this case, constructive mathematical models of natural processes are used, which more realistically describe the trajectories of diffusion-type processes, rather than those of the Wiener process. We examine models where particles have some free distance between two consecutive collisions. At the same time, we investigate two cases: the Markov evolutionary system, where the time during which the particle moves towards some direction is distributed exponentially with intensity parameter λ; and the semi-Markov evolutionary system, with arbitrary distribution of the switching process. Thus, the models investigated here describe the motion of particles with a finite speed and the proposed random evolutionary process with characteristics of a natural physical process: free run and finite propagation speed. In the proposed models, the number of possible directions of evolution can be finite or infinite.
