Semi Markov Random Evolutions
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Semi Markov Random Evolutions
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Author : Vladimir S. Korolyuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Semi Markov Random Evolutions written by Vladimir S. Korolyuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The evolution of systems in random media is a broad and fruitful field for the applica tions of different mathematical methods and theories. This evolution can be character ized by a semigroup property. In the abstract form, this property is given by a semigroup of operators in a normed vector (Banach) space. In the practically boundless variety of mathematical models of the evolutionary systems, we have chosen the semi-Markov ran dom evolutions as an object of our consideration. The definition of the evolutions of this type is based on rather simple initial assumptions. The random medium is described by the Markov renewal processes or by the semi Markov processes. The local characteristics of the system depend on the state of the ran dom medium. At the same time, the evolution of the system does not affect the medium. Hence, the semi-Markov random evolutions are described by two processes, namely, by the switching Markov renewal process, which describes the changes of the state of the external random medium, and by the switched process, i.e., by the semigroup of oper ators describing the evolution of the system in the semi-Markov random medium.
Discrete Time Semi Markov Random Evolutions And Their Applications
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Author : Nikolaos Limnios
language : en
Publisher: Springer Nature
Release Date : 2023-07-24
Discrete Time Semi Markov Random Evolutions And Their Applications written by Nikolaos Limnios and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-24 with Mathematics categories.
This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.
Random Evolutions And Their Applications
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Author : Anatoly Swishchuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Random Evolutions And Their Applications written by Anatoly Swishchuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The main purpose of this handbook is to summarize and to put in order the ideas, methods, results and literature on the theory of random evolutions and their applications to the evolutionary stochastic systems in random media, and also to present some new trends in the theory of random evolutions and their applications. In physical language, a random evolution ( RE ) is a model for a dynamical sys tem whose state of evolution is subject to random variations. Such systems arise in all branches of science. For example, random Hamiltonian and Schrodinger equations with random potential in quantum mechanics, Maxwell's equation with a random refractive index in electrodynamics, transport equations associated with the trajec tory of a particle whose speed and direction change at random, etc. There are the examples of a single abstract situation in which an evolving system changes its "mode of evolution" or "law of motion" because of random changes of the "environment" or in a "medium". So, in mathematical language, a RE is a solution of stochastic operator integral equations in a Banach space. The operator coefficients of such equations depend on random parameters. Of course, in such generality , our equation includes any homogeneous linear evolving system. Particular examples of such equations were studied in physical applications many years ago. A general mathematical theory of such equations has been developed since 1969, the Theory of Random Evolutions.
Evolution Of Systems In Random Media
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Author : Vladimir S. Korolyuk
language : en
Publisher: CRC Press
Release Date : 1995-09-11
Evolution Of Systems In Random Media written by Vladimir S. Korolyuk and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-11 with Mathematics categories.
Evolution of Systems in Random Media is an innovative, application-oriented text that explores stochastic models of evolutionary stochastic systems in random media. Specially designed for researchers and practitioners who do not have a background in random evolutions, the book allows non-experts to explore the potential information and applications that random evolutions can provide.
Limit Theorems For Randomly Stopped Stochastic Processes
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Author : Dmitrii S. Silvestrov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Limit Theorems For Randomly Stopped Stochastic Processes written by Dmitrii S. Silvestrov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Limit theorems for stochastic processes are an important part of probability theory and mathematical statistics and one model that has attracted the attention of many researchers working in the area is that of limit theorems for randomly stopped stochastic processes. This volume is the first to present a state-of-the-art overview of this field, with many of the results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast, and technically demanding, Russian literature in detail. A survey of the literature and an extended bibliography of works in the area are also provided. The coverage is thorough, streamlined and arranged according to difficulty for use as an upper-level text if required. It is an essential reference for theoretical and applied researchers in the fields of probability and statistics that will contribute to the continuing extensive studies in the area andremain relevant for years to come.
Inhomogeneous Random Evolutions And Their Applications
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Author : Anatoliy Swishchuk
language : en
Publisher: CRC Press
Release Date : 2019-12-11
Inhomogeneous Random Evolutions And Their Applications written by Anatoliy Swishchuk and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-11 with Mathematics categories.
Inhomogeneous Random Evolutions and Their Applications explains how to model various dynamical systems in finance and insurance with non-homogeneous in time characteristics. It includes modeling for: financial underlying and derivatives via Levy processes with time-dependent characteristics; limit order books in the algorithmic and HFT with counting price changes processes having time-dependent intensities; risk processes which count number of claims with time-dependent conditional intensities; multi-asset price impact from distressed selling; regime-switching Levy-driven diffusion-based price dynamics. Initial models for those systems are very complicated, which is why the author’s approach helps to simplified their study. The book uses a very general approach for modeling of those systems via abstract inhomogeneous random evolutions in Banach spaces. To simplify their investigation, it applies the first averaging principle (long-run stability property or law of large numbers [LLN]) to get deterministic function on the long run. To eliminate the rate of convergence in the LLN, it uses secondly the functional central limit theorem (FCLT) such that the associated cumulative process, centered around that deterministic function and suitably scaled in time, may be approximated by an orthogonal martingale measure, in general; and by standard Brownian motion, in particular, if the scale parameter increases. Thus, this approach allows the author to easily link, for example, microscopic activities with macroscopic ones in HFT, connecting the parameters driving the HFT with the daily volatilities. This method also helps to easily calculate ruin and ultimate ruin probabilities for the risk process. All results in the book are new and original, and can be easily implemented in practice.
Discrete Time Semi Markov Random Evolutions And Their Applications
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Author : Nikolaos Limnios
language : en
Publisher:
Release Date : 2023
Discrete Time Semi Markov Random Evolutions And Their Applications written by Nikolaos Limnios and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.
Exploring Stochastic Laws
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Author : A.V. Skorokhod
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-05-18
Exploring Stochastic Laws written by A.V. Skorokhod and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-18 with Law categories.
No detailed description available for "Exploring Stochastic Laws".
Data Driven Modeling For Sustainable Engineering
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Author : Kondo H. Adjallah
language : en
Publisher: Springer
Release Date : 2019-06-21
Data Driven Modeling For Sustainable Engineering written by Kondo H. Adjallah and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-21 with Technology & Engineering categories.
This book gathers the proceedings of the 1st International Conference on Engineering, Applied Sciences and System Modeling (ICEASSM), a four-day event (18th–21st April 2017) held in Accra, Ghana. It focuses on research work promoting a better understanding of engineering problems through applied sciences and modeling, and on solutions generated in an African setting but with relevance to the world as a whole. The book provides a holistic overview of challenges facing Africa, and addresses various areas from research and development perspectives. Presenting contributions by scientists, engineers and experts hailing from a host of international institutions, the book offers original approaches and technological solutions to help solve real-world problems through research and knowledge sharing. Further, it explores promising opportunities for collaborative research on issues of scientific, economic and social development, making it of interest to researchers, scientists and practitioners looking to conduct research in disciplines such as water supply, control, civil engineering, statistical modeling, renewable energy and sustainable urban development.
Matrix Analytic Methods In Stochastic Models
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Author : S. Chakravarthy
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Matrix Analytic Methods In Stochastic Models written by S. Chakravarthy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
Based on the proceedings of the first International Conference on Matrix-Analytic Methods (MAM) in Stochastic Models, held in Flint, Michigan, this book presents a general working knowledge of MAM through tutorial articles and application papers. It furnishes information on MAM studies carried out in the former Soviet Union.