random dynamical systems theory and applications

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Random Dynamical Systems

Author : Rabi Bhattacharya
ISBN : 9781139461627
Genre : Mathematics
File Size : 62. 15 MB
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This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.

Monotone Random Systems Theory And Applications

Author : Igor Chueshov
ISBN : 9783540458159
Genre : Mathematics
File Size : 81. 35 MB
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The aim of this book is to present a recently developed approach suitable for investigating a variety of qualitative aspects of order-preserving random dynamical systems and to give the background for further development of the theory. The main objects considered are equilibria and attractors. The effectiveness of this approach is demonstrated by analysing the long-time behaviour of some classes of random and stochastic ordinary differential equations which arise in many applications.

Random Dynamical Systems In Finance

Author : Anatoliy Swishchuk
ISBN : 9781439867198
Genre : Business & Economics
File Size : 54. 64 MB
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The theory and applications of random dynamical systems (RDS) are at the cutting edge of research in mathematics and economics, particularly in modeling the long-run evolution of economic systems subject to exogenous random shocks. Despite this interest, there are no books available that solely focus on RDS in finance and economics. Exploring this emerging area, Random Dynamical Systems in Finance shows how to model RDS in financial applications. Through numerous examples, the book explains how the theory of RDS can describe the asymptotic and qualitative behavior of systems of random and stochastic differential/difference equations in terms of stability, invariant manifolds, and attractors. The authors present many models of RDS and develop techniques for implementing RDS as approximations to financial models and option pricing formulas. For example, they approximate geometric Markov renewal processes in ergodic, merged, double-averaged, diffusion, normal deviation, and Poisson cases and apply the obtained results to option pricing formulas. With references at the end of each chapter, this book provides a variety of RDS for approximating financial models, presents numerous option pricing formulas for these models, and studies the stability and optimal control of RDS. The book is useful for researchers, academics, and graduate students in RDS and mathematical finance as well as practitioners working in the financial industry.

Random Dynamical Systems

Author : Ludwig Arnold
ISBN : 3540637583
Genre : Language Arts & Disciplines
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Background and Scope of the Book This book continues, extends, and unites various developments in the intersection of probability theory and dynamical systems. I will briefly outline the background of the book, thus placing it in a systematic and historical context and tradition. Roughly speaking, a random dynamical system is a combination of a measure-preserving dynamical system in the sense of ergodic theory, (D,F,lP', (B(t))tE'lf), 'II'= JR+, IR, z+, Z, with a smooth (or topological) dy namical system, typically generated by a differential or difference equation :i: = f(x) or Xn+l = tp(x.,), to a random differential equation :i: = f(B(t)w,x) or random difference equation Xn+l = tp(B(n)w, Xn)· Both components have been very well investigated separately. However, a symbiosis of them leads to a new research program which has only partly been carried out. As we will see, it also leads to new problems which do not emerge if one only looks at ergodic theory and smooth or topological dynam ics separately. From a dynamical systems point of view this book just deals with those dynamical systems that have a measure-preserving dynamical system as a factor (or, the other way around, are extensions of such a factor). As there is an invariant measure on the factor, ergodic theory is always involved.

Topological Dynamics Of Random Dynamical Systems

Author : Nguyen Dinh Cong
ISBN : 0198501579
Genre : Mathematics
File Size : 72. 67 MB
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This book is a systematic presentation of the solution of one of the fundamental problems of the theory of random dynamical systems - the problem of topological classification and structural stability of linear hyperbolic random dynamical systems. Employing the tools and methods of algebraic ergodic theory, the theory presented in the book has surprisingly beautiful results showing the richness of random dynamical systems as well as giving a gentle generalizationof the classical deterministic theory.

Stochastic Dynamics

Author : Hans Crauel
ISBN : 9780387226552
Genre : Mathematics
File Size : 60. 9 MB
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Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations. Example applications are presented from biology, chemistry and engineering, while describing numerical treatments of stochastic systems.

Stochastic Systems

Author : Vladimir Semenovich Pugachev
ISBN : 9810247427
Genre : Mathematics
File Size : 25. 4 MB
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General theory and basic methods of linear and nonlinear stocastic systems (StS), based on the equations for characteristic functions and functionals.Special attention is paid to methods based on canonical expansions and integral canonical represntations.

Advances In Control Systems

Author : C. T. Leondes
ISBN : 9781483194615
Genre : Technology & Engineering
File Size : 57. 88 MB
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Advances in Control Systems: Theory and Applications, Volume 7 provides information pertinent to the significant progress in the field of control and systems theory and applications. This book covers the important general area of computational problems in random and deterministic dynamic systems. Organized into six chapters, this volume begins with an overview of the controllability of a stochastic system. This text then presents a survey and status of methods for nonlinear minimal variance filtering. Other chapters consider some possible pitfalls and develop practical approximate nonlinear filters. This book discusses as well the area of computational problems and techniques for optimal nonlinear control problems. Computer simulation results are also included in order to show a number of the key results. The final chapter deals with the development of algorithms for the determination of the optimal control of distributed parameter systems, which pervades many areas of engineering endeavor. This book is a valuable resource for mathematicians and engineers.

Mathematics Of Complexity And Dynamical Systems

Author : Robert A. Meyers
ISBN : 9781461418054
Genre : Mathematics
File Size : 87. 59 MB
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Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Applied Nonautonomous And Random Dynamical Systems

Author : Tomás Caraballo
ISBN : 9783319492476
Genre : Mathematics
File Size : 41. 52 MB
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This book offers an introduction to the theory of non-autonomous and stochastic dynamical systems, with a focus on the importance of the theory in the Applied Sciences. It starts by discussing the basic concepts from the theory of autonomous dynamical systems, which are easier to understand and can be used as the motivation for the non-autonomous and stochastic situations. The book subsequently establishes a framework for non-autonomous dynamical systems, and in particular describes the various approaches currently available for analysing the long-term behaviour of non-autonomous problems. Here, the major focus is on the novel theory of pullback attractors, which is still under development. In turn, the third part represents the main body of the book, introducing the theory of random dynamical systems and random attractors and revealing how it may be a suitable candidate for handling realistic models with stochasticity. A discussion of future research directions serves to round out the coverage.

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