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Random Evolutions and Their Applications

Author: Anatoly Swishchuk

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 212

ISBN-13: 9401157545

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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.

Book Synopsis Random Evolutions and Their Applications by : Anatoly Swishchuk

Download or read book Random Evolutions and Their Applications written by Anatoly Swishchuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Inhomogeneous Random Evolutions and Their Applications

Author: Anatoliy Swishchuk

Publisher: CRC Press

Published: 2019-12-11

Total Pages: 253

ISBN-13: 0429855052

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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.

Book Synopsis Inhomogeneous Random Evolutions and Their Applications by : Anatoliy Swishchuk

Download or read book Inhomogeneous Random Evolutions and Their Applications written by Anatoliy Swishchuk and published by CRC Press. This book was released on 2019-12-11 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author: Nikolaos Limnios

Publisher: Springer Nature

Published: 2023-07-24

Total Pages: 206

ISBN-13: 3031334299

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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.

Book Synopsis Discrete-Time Semi-Markov Random Evolutions and Their Applications by : Nikolaos Limnios

Download or read book Discrete-Time Semi-Markov Random Evolutions and Their Applications written by Nikolaos Limnios and published by Springer Nature. This book was released on 2023-07-24 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author: Anatoly Swishchuk

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 310

ISBN-13: 9401595984

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The book is devoted to the new trends in random evolutions and their various applications to stochastic evolutionary sytems (SES). Such new developments as the analogue of Dynkin's formulae, boundary value problems, stochastic stability and optimal control of random evolutions, stochastic evolutionary equations driven by martingale measures are considered. The book also contains such new trends in applied probability as stochastic models of financial and insurance mathematics in an incomplete market. In the famous classical financial mathematics Black-Scholes model of a (B,S) market for securities prices, which is used for the description of the evolution of bonds and stocks prices and also for their derivatives, such as options, futures, forward contracts, etc., it is supposed that the dynamic of bonds and stocks prices are set by a linear differential and linear stochastic differential equations, respectively, with interest rate, appreciation rate and volatility such that they are predictable processes. Also, in the Arrow-Debreu economy, the securities prices which support a Radner dynamic equilibrium are a combination of an Ito process and a random point process, with the all coefficients and jumps being predictable processes.

Book Synopsis Random Evolutions and their Applications by : Anatoly Swishchuk

Download or read book Random Evolutions and their Applications written by Anatoly Swishchuk and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the new trends in random evolutions and their various applications to stochastic evolutionary sytems (SES). Such new developments as the analogue of Dynkin's formulae, boundary value problems, stochastic stability and optimal control of random evolutions, stochastic evolutionary equations driven by martingale measures are considered. The book also contains such new trends in applied probability as stochastic models of financial and insurance mathematics in an incomplete market. In the famous classical financial mathematics Black-Scholes model of a (B,S) market for securities prices, which is used for the description of the evolution of bonds and stocks prices and also for their derivatives, such as options, futures, forward contracts, etc., it is supposed that the dynamic of bonds and stocks prices are set by a linear differential and linear stochastic differential equations, respectively, with interest rate, appreciation rate and volatility such that they are predictable processes. Also, in the Arrow-Debreu economy, the securities prices which support a Radner dynamic equilibrium are a combination of an Ito process and a random point process, with the all coefficients and jumps being predictable processes.

Inhomogeneous Random Evolutions and Their Applications

Author: Anatoliĭ Vitalʹevich Svishchuk

Publisher:

Published: 2020

Total Pages: 0

ISBN-13:

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"The book deals with inhomogeneous REs and their applications, which are more general and more applicable because they describe in a much better way the evolutions of many processes in real world, which have no homogeneous evolution/behaviour, including economics, finance and insurance"--Provided by publisher.

Book Synopsis Inhomogeneous Random Evolutions and Their Applications by : Anatoliĭ Vitalʹevich Svishchuk

Download or read book Inhomogeneous Random Evolutions and Their Applications written by Anatoliĭ Vitalʹevich Svishchuk and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book deals with inhomogeneous REs and their applications, which are more general and more applicable because they describe in a much better way the evolutions of many processes in real world, which have no homogeneous evolution/behaviour, including economics, finance and insurance"--Provided by publisher.

Semi-Markov Random Evolutions

Author: Vladimir S. Korolyuk

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 315

ISBN-13: 9401110107

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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.

Book Synopsis Semi-Markov Random Evolutions by : Vladimir S. Korolyuk

Download or read book Semi-Markov Random Evolutions written by Vladimir S. Korolyuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Evolution of Biological Systems in Random Media: Limit Theorems and Stability

Author: Anatoly Swishchuk

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 230

ISBN-13: 9401715068

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This is a new book in biomathematics, which includes new models of stochastic non-linear biological systems and new results for these systems. These results are based on the new results for non-linear difference and differential equations in random media. This book contains: -New stochastic non-linear models of biological systems, such as biological systems in random media: epidemic, genetic selection, demography, branching, logistic growth and predator-prey models; -New results for scalar and vector difference equations in random media with applications to the stochastic biological systems in 1); -New results for stochastic non-linear biological systems, such as averaging, merging, diffusion approximation, normal deviations and stability; -New approach to the study of stochastic biological systems in random media such as random evolution approach.

Book Synopsis Evolution of Biological Systems in Random Media: Limit Theorems and Stability by : Anatoly Swishchuk

Download or read book Evolution of Biological Systems in Random Media: Limit Theorems and Stability written by Anatoly Swishchuk and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a new book in biomathematics, which includes new models of stochastic non-linear biological systems and new results for these systems. These results are based on the new results for non-linear difference and differential equations in random media. This book contains: -New stochastic non-linear models of biological systems, such as biological systems in random media: epidemic, genetic selection, demography, branching, logistic growth and predator-prey models; -New results for scalar and vector difference equations in random media with applications to the stochastic biological systems in 1); -New results for stochastic non-linear biological systems, such as averaging, merging, diffusion approximation, normal deviations and stability; -New approach to the study of stochastic biological systems in random media such as random evolution approach.

Evolution of Systems in Random Media

Author: Vladimir S. Korolyuk

Publisher: CRC Press

Published: 1995-09-11

Total Pages: 358

ISBN-13: 9780849394058

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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.

Book Synopsis Evolution of Systems in Random Media by : Vladimir S. Korolyuk

Download or read book Evolution of Systems in Random Media written by Vladimir S. Korolyuk and published by CRC Press. This book was released on 1995-09-11 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Evolution Algebras and Their Applications

Author: Jianjun Paul Tian

Publisher: Springer Science & Business Media

Published: 2008

Total Pages: 136

ISBN-13: 3540742832

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Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.

Book Synopsis Evolution Algebras and Their Applications by : Jianjun Paul Tian

Download or read book Evolution Algebras and Their Applications written by Jianjun Paul Tian and published by Springer Science & Business Media. This book was released on 2008 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.

Evolution of Engineering and Information Systems and Their Applications

Author: Lakhmi C. Jain

Publisher: CRC Press

Published: 1999-09-24

Total Pages: 334

ISBN-13: 9780849319655

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Worldwide interest in the applications of evolutionary computing techniques to the design of engineering and information systems grows each day. Pattern recognition, control systems, factory scheduling, automation, generation of computer programs, and the design of intelligent paradigms all benefit from evolutionary techniques-their potential applications indeed seem limited only by the imaginations of scientists and engineers. This is an area of intensive research and development, and evolutionary computing techniques are themselves constantly evolving. It becomes important, then, that computer scientists and applications engineers have a working knowledge of the techniques, stay abreast of recent advances, and have the opportunity to incorporate them into their own systems and designs. Evolution of Engineering and Information Systems and Their Applications fills this need by providing an overview of the field and offering state-of-the-art reviews of the most important techniques and applications of evolutionary computing. The top experts from around the world discuss developments in genetic algorithms, genetic programming, and evolutionary strategies and applications including VLSI CAD, robot sensors, neural networks, and fuzzy classification systems. This is a new and very hot field, yet there are few-if any-resources that document and disseminate its advances. With Evolution of Engineering and Information Systems and Their Applications, you have the opportunity to learn from the leading authorities, use these powerful techniques to improve your own systems, and help evolutionary computing reach its nearly boundless potential.

Book Synopsis Evolution of Engineering and Information Systems and Their Applications by : Lakhmi C. Jain

Download or read book Evolution of Engineering and Information Systems and Their Applications written by Lakhmi C. Jain and published by CRC Press. This book was released on 1999-09-24 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Worldwide interest in the applications of evolutionary computing techniques to the design of engineering and information systems grows each day. Pattern recognition, control systems, factory scheduling, automation, generation of computer programs, and the design of intelligent paradigms all benefit from evolutionary techniques-their potential applications indeed seem limited only by the imaginations of scientists and engineers. This is an area of intensive research and development, and evolutionary computing techniques are themselves constantly evolving. It becomes important, then, that computer scientists and applications engineers have a working knowledge of the techniques, stay abreast of recent advances, and have the opportunity to incorporate them into their own systems and designs. Evolution of Engineering and Information Systems and Their Applications fills this need by providing an overview of the field and offering state-of-the-art reviews of the most important techniques and applications of evolutionary computing. The top experts from around the world discuss developments in genetic algorithms, genetic programming, and evolutionary strategies and applications including VLSI CAD, robot sensors, neural networks, and fuzzy classification systems. This is a new and very hot field, yet there are few-if any-resources that document and disseminate its advances. With Evolution of Engineering and Information Systems and Their Applications, you have the opportunity to learn from the leading authorities, use these powerful techniques to improve your own systems, and help evolutionary computing reach its nearly boundless potential.