Inhomogeneous Random Evolutions and Their Applications

Inhomogeneous Random Evolutions and Their Applications

Author: Anatoliy Swishchuk

Publisher: CRC Press

Published: 2019-12-11

Total Pages: 253

ISBN-13: 0429855052

DOWNLOAD EBOOK

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.

Inhomogeneous Random Evolutions and Their Applications

Inhomogeneous Random Evolutions and Their Applications

Author: Anatoliĭ Vitalʹevich Svishchuk

Publisher:

Published: 2020

Total Pages: 0

ISBN-13:

DOWNLOAD EBOOK

"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.

Random Evolutions and Their Applications

Random Evolutions and Their Applications

Author: Anatoly Swishchuk

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 212

ISBN-13: 9401157545

DOWNLOAD EBOOK

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.

Discrete-Time Semi-Markov Random Evolutions and Their Applications

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

DOWNLOAD EBOOK

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 Motions in Markov and Semi-Markov Random Environments 1

Random Motions in Markov and Semi-Markov Random Environments 1

Author: Anatoliy Pogorui

Publisher: John Wiley & Sons

Published: 2021-03-16

Total Pages: 256

ISBN-13: 178630547X

DOWNLOAD EBOOK

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.


Book Synopsis Random Motions in Markov and Semi-Markov Random Environments 1 by : Anatoliy Pogorui

Download or read book Random Motions in Markov and Semi-Markov Random Environments 1 written by Anatoliy Pogorui and published by John Wiley & Sons. This book was released on 2021-03-16 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

The Seventh European Conference on Combinatorics, Graph Theory and Applications

Author: Jaroslav Nešetřil

Publisher: Springer Science & Business Media

Published: 2014-01-18

Total Pages: 600

ISBN-13: 887642475X

DOWNLOAD EBOOK

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.


Book Synopsis The Seventh European Conference on Combinatorics, Graph Theory and Applications by : Jaroslav Nešetřil

Download or read book The Seventh European Conference on Combinatorics, Graph Theory and Applications written by Jaroslav Nešetřil and published by Springer Science & Business Media. This book was released on 2014-01-18 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Trotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications

Trotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications

Author: T. E. Govindan

Publisher: Springer Nature

Published:

Total Pages: 321

ISBN-13: 3031427912

DOWNLOAD EBOOK


Book Synopsis Trotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications by : T. E. Govindan

Download or read book Trotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications written by T. E. Govindan and published by Springer Nature. This book was released on with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Data Science, Learning by Latent Structures, and Knowledge Discovery

Data Science, Learning by Latent Structures, and Knowledge Discovery

Author: Berthold Lausen

Publisher: Springer

Published: 2015-05-06

Total Pages: 552

ISBN-13: 3662449838

DOWNLOAD EBOOK

This volume comprises papers dedicated to data science and the extraction of knowledge from many types of data: structural, quantitative, or statistical approaches for the analysis of data; advances in classification, clustering and pattern recognition methods; strategies for modeling complex data and mining large data sets; applications of advanced methods in specific domains of practice. The contributions offer interesting applications to various disciplines such as psychology, biology, medical and health sciences; economics, marketing, banking and finance; engineering; geography and geology; archeology, sociology, educational sciences, linguistics and musicology; library science. The book contains the selected and peer-reviewed papers presented during the European Conference on Data Analysis (ECDA 2013) which was jointly held by the German Classification Society (GfKl) and the French-speaking Classification Society (SFC) in July 2013 at the University of Luxembourg.


Book Synopsis Data Science, Learning by Latent Structures, and Knowledge Discovery by : Berthold Lausen

Download or read book Data Science, Learning by Latent Structures, and Knowledge Discovery written by Berthold Lausen and published by Springer. This book was released on 2015-05-06 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises papers dedicated to data science and the extraction of knowledge from many types of data: structural, quantitative, or statistical approaches for the analysis of data; advances in classification, clustering and pattern recognition methods; strategies for modeling complex data and mining large data sets; applications of advanced methods in specific domains of practice. The contributions offer interesting applications to various disciplines such as psychology, biology, medical and health sciences; economics, marketing, banking and finance; engineering; geography and geology; archeology, sociology, educational sciences, linguistics and musicology; library science. The book contains the selected and peer-reviewed papers presented during the European Conference on Data Analysis (ECDA 2013) which was jointly held by the German Classification Society (GfKl) and the French-speaking Classification Society (SFC) in July 2013 at the University of Luxembourg.

The Ocean Surface

The Ocean Surface

Author: Y. Toba

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 581

ISBN-13: 940157717X

DOWNLOAD EBOOK


Book Synopsis The Ocean Surface by : Y. Toba

Download or read book The Ocean Surface written by Y. Toba and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Networks and their Applications

Complex Networks and their Applications

Author: Hocine Cherifi

Publisher: Cambridge Scholars Publishing

Published: 2014-06-30

Total Pages: 355

ISBN-13: 1443863246

DOWNLOAD EBOOK

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.


Book Synopsis Complex Networks and their Applications by : Hocine Cherifi

Download or read book Complex Networks and their Applications written by Hocine Cherifi and published by Cambridge Scholars Publishing. This book was released on 2014-06-30 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.