Inhomogeneous Random Evolutions And Their Applications
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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.
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.
Inhomogeneous Random Evolutions And Their Applications
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Author : Anatoliĭ Vitalʹevich Svishchuk
language : en
Publisher:
Release Date : 2020
Inhomogeneous Random Evolutions And Their Applications written by Anatoliĭ Vitalʹevich Svishchuk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Banach spaces categories.
"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.
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 Motions In Markov And Semi Markov Random Environments 1
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Author : Anatoliy Pogorui
language : en
Publisher: John Wiley & Sons
Release Date : 2021-03-16
Random Motions In Markov And Semi Markov Random Environments 1 written by Anatoliy Pogorui and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-16 with Mathematics categories.
This book is the first of two volumes on random motions in Markov and semi-Markov random environments. This first volume focuses on homogenous random motions. This volume consists of two parts, the first describing the basic concepts and methods that have been developed for random evolutions. These methods are the foundational tools used in both volumes, and this description includes many results in potential operators. Some techniques to find closed-form expressions in relevant applications are also presented. The second part deals with asymptotic results and presents a variety of applications, including random motion with different types of boundaries, the reliability of storage systems and solutions of partial differential equations with constant coefficients, using commutative algebra techniques. It also presents an alternative formulation to the Black-Scholes formula in finance, fading evolutions and telegraph processes, including jump telegraph processes and the estimation of the number of level crossings for telegraph processes.
The Seventh European Conference On Combinatorics Graph Theory And Applications
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Author : Jaroslav Nešetřil
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-18
The Seventh European Conference On Combinatorics Graph Theory And Applications written by Jaroslav Nešetřil 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 2014-01-18 with Mathematics categories.
In the tradition of EuroComb'01 (Barcelona), Eurocomb'03 (Prague), EuroComb'05 (Berlin), Eurocomb'07 (Seville), Eurocomb'09 (Bordeaux), and Eurocomb'11 (Budapest), this volume covers recent advances in combinatorics and graph theory including applications in other areas of mathematics, computer science and engineering. Topics include, but are not limited to: Algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, ordered sets, random methods, topological combinatorics.
Complex Networks And Their Applications
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Author : Hocine Cherifi
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2014-06-30
Complex Networks And Their Applications written by Hocine Cherifi and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-30 with Mathematics categories.
Fuelled by the big data paradigm, the study of networks is an interdisciplinary field that is growing at the interface of many branches of science including mathematics, physics, computer science, biology, economics and the social sciences. This book, written by experts from the Network Science community, covers a wide range of theoretical and practical advances in this highly active field, highlighting the strong interconnections between works in different disciplines. The eleven chapters take the reader through the essential concepts for the structural analysis of networks, and their applications to real-world scenarios. Being self-contained, the book is intended for researchers, graduate and advanced undergraduate students from different intellectual backgrounds. Each chapter combines mathematical rigour with rich references to the literature, while remaining accessible to a wide range of readers who wish to understand some of the key issues encountered in many aspects of networked everyday life.
Complex Networks Their Applications X
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Author : Rosa Maria Benito
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Complex Networks Their Applications X written by Rosa Maria Benito and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Technology & Engineering categories.
This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students, and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the X International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2021). The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks, and technological networks.
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.
Trotter Kato Approximations Of Stochastic Differential Equations In Infinite Dimensions And Applications
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Author : T. E. Govindan
language : en
Publisher: Springer Nature
Release Date : 2024-07-01
Trotter Kato Approximations Of Stochastic Differential Equations In Infinite Dimensions And Applications written by T. E. Govindan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-01 with Mathematics categories.
This is the first comprehensive book on Trotter-Kato approximations of stochastic differential equations (SDEs) in infinite dimensions and applications. This research monograph brings together the varied literature on this topic since 1985 when such a study was initiated. The author provides a clear and systematic introduction to the theory of Trotter-Kato approximations of SDEs and also presents its applications to practical topics such as stochastic stability and stochastic optimal control. The theory assimilated here is developed slowly and methodically in digestive pieces. The book begins with a motivational chapter introducing several different models that highlight the importance of the theory on abstract SDEs that will be considered in the subsequent chapters. The author next introduces the necessary mathematical background and then leads the reader into the main discussion of the monograph, namely, the Trotter-Kato approximations of many classes of SDEs in Hilbert spaces, Trotter-Kato approximations of SDEs in UMD Banach spaces and some of their applications. Most of the results presented in the main chapters appear for the first time in a book form. The monograph also contains many illustrative examples on stochastic partial differential equations and one in finance as an application of the Trotter-Kato formula. The key steps are included in all proofs which will help the reader to get a real insight into the theory of Trotter-Kato approximations and its use. This book is intended for researchers and graduate students in mathematics specializing in probability theory. It will also be useful to numerical analysts, engineers, physicists and practitioners who are interested in applying the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is accessible to a wider audience including non-specialists in stochastic processes.