Описание: This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the "Four Step Scheme", and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.
Описание: Presents a different approach to the modelling, synthesis and numerical simulation of random processes with applications in communications and related fields. This book provides an account of random processes from an engineering point of view and illustrates the concepts with examples taken from the communications area.
Описание: In the last century many problems which arose in the science, engineering and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to (i). ordinary differential equations which are singular in the independent and/or dependent variables together with initial and boundary conditions, and (ii). Volterra and Fredholm type integral equations. As one might expect general existence results were difficult to establish for the problems which arose. Indeed until the early 1990's only very special examples were examined and these examples were usually tackled using some special device, which was usually only applicable to the particular problem under investigation. However in the 1990's new results in inequality and fixed point theory were used to present a very general existence theory for singular problems. This monograph presents an up to date account of the literature on singular problems. One of our aims also is to present recent theory on singular differential and integral equations to a new and wider audience. The book presents a compact, thorough, and self-contained account for singular problems. An important feature of this book is that we illustrate how easily the theory can be applied to discuss many real world examples of current interest.
Описание: During the past three decades, the development of nonlinear analysis, dynamical systems and their applications to science and engineering has stimulated renewed enthusiasm for the theory of Ordinary Differential Equations (ODE).This useful book, which is based on the lecture notes of a well-received graduate course, emphasizes both theory and applications, taking numerous examples from physics and biology to illustrate the application of ODE theory and techniques.Written in a straightforward and easily accessible style, this volume presents dynamical systems in the spirit of nonlinear analysis to readers at a graduate level and serves both as a textbook and as a valuable resource for researchers.This new edition contains corrections and suggestions from the various readers and users. A new chapter on Monotone Dynamical Systems is added to take into account the new developments in ordinary differential equations and dynamical systems.
Описание: Presents an introduction to applications of Lie groups to differential equations which have proved to be useful in practice. Following an exposition of the applications, this book develops the underlying theory, with many of the topics presented in a novel way, emphasizing explicit examples and computations.
Описание: Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as
stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well
established, the study of their stability properties has grown rapidly only in the past 20 years, and most results have remained scattered in journals and conference proceedings.This
book offers a systematic presentation of the modern theory of the stability of stochastic differential equations in infinite dimensional spaces - particularly Hilbert spaces. The treatment
includes a review of basic concepts and investigation of the stability theory of linear and nonlinear stochastic differential equations and stochastic functional differential equations in
The final chapter of this title explores topics and applications such as stochastic optimal control and feedback stabilization, stochastic reaction-diffusion,
Navier-Stokes equations, and stochastic population dynamics. In recent years, this area of study has become the focus of increasing attention, and the relevant literature has
expanded greatly. "Stability of Infinite Dimensional Stochastic Differential Equations with Applications" makes up-to-date material in this important field accessible even to newcomers
and lays the foundation for future advances.
Описание: A secret traveller to the Tibetan capital of Lhasa, the author was forced to live, dress and behave as a Tibetan in order to remain undetected. Because of his unique perspective, he was able to provide an excellent description of the diplomatic, political, military and industrial situation of the country in the 1920s. Provides developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus. This book is application oriented and it contains the theory of Fractional Differential Equations. It provides problems and directions for further investigations.
Описание: Contains the written versions of lectures delivered since 1997 in the weekly seminar on Applied Mathematics at the College de France in Paris, directed by Jacques-Louis Lions. This book includes texts that deal with various aspects of the theory of nonlinear partial differential equations.
Описание: This book provides a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as important applications of the theory. The text is written to be used in the traditional way (emphasis on the theory with the computer component as optional) or in a more applied way (emphasis on the applications and the computer material). The accompanying CD contains Maple worksheets to use in working the exercises and extending the examples. The disk also contains special Maple code for performing various tasks. In addition to its use in a traditional one- or two- (there is enough material for two) semester graduate course in mathematics, the book is organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering. Researchers and professionals may also find the supplementary material on the disk on discrete dynamical systems, theory of iterated maps, and code for performing specific tasks on the disks particularly useful.
Описание: List of figures. Preface. Contributing Authors. Introduction.- 1. History of Delay Equations; J.K. Hale.- Part I General Results and Linear Theory of Delay Equations in Finite Dimensional Spaces. 2. Some General Results and Remarks on Delay Differential Equations; E. Ait Dads. 3. Linear Autonomous Functional Differential Equations; F. Kappel.- Part II Hopf Bifurcation, Centre Manifolds and Normal Forms for Delay Differential Equations. 4. Variation of Constant Formula for Delay Differential Equations; M.L. Hbid, K. Ezzinbi. 5. Introduction to Hopf Bifurcation Theory for Delay Differential Equations; M.L. Hbid. 6. An Algorithmic Scheme for Approximating Center Manifolds and Normal Forms for Functional Differential Equations; M. Ait Babram. 7. Normal Forms and Bifurcations for Delay Differential Equations; T. Faria.- Part III Functional Differential Equations in Infinite Dimensional Spaces. 8. A Theory of Linear Delay Differential Equations in Infinite Dimensional Spaces; O. Arino, E. Sanchez. 9. The Basic Theory of Abstract Semilinear Functional Differential Equations with Non-Dense Domain; K. Ezzinbi, M. Adimy.- Part IV More on Delay Differential Equations and Applications. 10. Dynamics of Delay Differential Equations; H.O. Walther. 11. Delay Differential Equations in Single Species Dynamics; Sh. Ruan. 12. Well-Posedness, Regularity and Asymptotic Behaviour of Retarded Differential Equations by Extrapolation Theory; L. Maniar.- References.- Index.
Описание: Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.
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