Stability Of Infinite Dimensional Stochastic Differential Equations With Applications
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Stability Of Infinite Dimensional Stochastic Differential Equations With Applications
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Author : Kai Liu
language : en
Publisher: CRC Press
Release Date : 2005-08-23
Stability Of Infinite Dimensional Stochastic Differential Equations With Applications written by Kai Liu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-23 with Mathematics categories.
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 establ
Stochastic Differential Equations In Infinite Dimensions
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Author : Leszek Gawarecki
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-29
Stochastic Differential Equations In Infinite Dimensions written by Leszek Gawarecki 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 2010-11-29 with Mathematics categories.
The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.
Stochastic Partial Differential Equations And Applications
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Author : Giuseppe Da Prato
language : en
Publisher: CRC Press
Release Date : 2002-04-05
Stochastic Partial Differential Equations And Applications written by Giuseppe Da Prato and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-05 with Mathematics categories.
Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.
Asiasim 2012
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Author : Tianyuan Xiao
language : en
Publisher: Springer
Release Date : 2012-10-08
Asiasim 2012 written by Tianyuan Xiao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-08 with Computers categories.
The Three-Volume-Set CCIS 323, 324, 325 (AsiaSim 2012) together with the Two-Volume-Set CCIS 326, 327 (ICSC 2012) constitutes the refereed proceedings of the Asia Simulation Conference, AsiaSim 2012, and the International Conference on System Simulation, ICSC 2012, held in Shanghai, China, in October 2012. The 267 revised full papers presented were carefully reviewed and selected from 906 submissions. The papers are organized in topical sections on modeling theory and technology; modeling and simulation technology on synthesized environment and virtual reality environment; pervasive computing and simulation technology; embedded computing and simulation technology; verification, validation and accreditation technology; networked modeling and simulation technology; modeling and simulation technology of continuous system, discrete system, hybrid system, and intelligent system; high performance computing and simulation technology; cloud simulation technology; modeling and simulation technology of complex system and open, complex, huge system; simulation based acquisition and virtual prototyping engineering technology; simulator; simulation language and intelligent simulation system; parallel and distributed software; CAD, CAE, CAM, CIMS, VP, VM, and VR; visualization; computing and simulation applications in science and engineering; computing and simulation applications in management, society and economics; computing and simulation applications in life and biomedical engineering; computing and simulation applications in energy and environment; computing and simulation applications in education; computing and simulation applications in military field; computing and simulation applications in medical field.
Applied Nonautonomous And Random Dynamical Systems
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Author : Tomás Caraballo
language : en
Publisher: Springer
Release Date : 2017-01-31
Applied Nonautonomous And Random Dynamical Systems written by Tomás Caraballo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-31 with Mathematics categories.
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.
Robust Engineering Designs Of Partial Differential Systems And Their Applications
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Author : Bor-Sen Chen
language : en
Publisher: CRC Press
Release Date : 2021-12-22
Robust Engineering Designs Of Partial Differential Systems And Their Applications written by Bor-Sen Chen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-22 with Mathematics categories.
Most systems in science, engineering, and biology are of partial differential systems (PDSs) modeled by partial differential equations. Many books about partial differential equations have been written by mathematicians and mainly address some fundamental mathematic backgrounds and discuss some mathematic properties of partial differential equations. Only a few books on PDSs have been written by engineers; however, these books have focused mainly on the theoretical stabilization analysis of PDSs, especially mechanical systems. This book investigates both robust stabilization control design and robust filter design and reference tracking control design in mechanical, signal processing, and control systems to fill a gap in the study of PDSs. Robust Engineering Designs of Partial Differential Systems and Their Applications offers some fundamental background in the first two chapters. The rest of the chapters focus on a specific design topic with a corresponding deep investigation into robust H∞ filtering, stabilization, or tracking design for more complex and practical PDSs under stochastic fluctuation and external disturbance. This book is aimed at engineers and scientists and addresses the gap between the theoretical stabilization results of PDSs in academic and practical engineering designs more focused on the robust H∞ filtering, stabilization, and tracking control problems of linear and nonlinear PDSs under intrinsic random fluctuation and external disturbance in industrial applications. Part I provides backgrounds on PDSs, such as Galerkin’s, and finite difference methods to approximate PDSs and a fuzzy method to approximate nonlinear PDSs. Part II examines robust H∞ filter designs for the robust state estimation of linear and nonlinear stochastic PDSs. And Part III treats robust H∞ stabilization and tracking control designs of linear and nonlinear PDSs. Every chapter focuses on an engineering design topic with both theoretical design analysis and practical design examples.
Discovering Evolution Equations With Applications
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Author : Mark McKibben
language : en
Publisher: CRC Press
Release Date : 2011-06-03
Discovering Evolution Equations With Applications written by Mark McKibben and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-03 with Mathematics categories.
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversation
Stochastic Partial Differential Equations Second Edition
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Author : Pao-Liu Chow
language : en
Publisher: CRC Press
Release Date : 2014-12-10
Stochastic Partial Differential Equations Second Edition written by Pao-Liu Chow and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-10 with Mathematics categories.
Explore Theory and Techniques to Solve Physical, Biological, and Financial Problems Since the first edition was published, there has been a surge of interest in stochastic partial differential equations (PDEs) driven by the Lévy type of noise. Stochastic Partial Differential Equations, Second Edition incorporates these recent developments and improves the presentation of material. New to the Second Edition Two sections on the Lévy type of stochastic integrals and the related stochastic differential equations in finite dimensions Discussions of Poisson random fields and related stochastic integrals, the solution of a stochastic heat equation with Poisson noise, and mild solutions to linear and nonlinear parabolic equations with Poisson noises Two sections on linear and semilinear wave equations driven by the Poisson type of noises Treatment of the Poisson stochastic integral in a Hilbert space and mild solutions of stochastic evolutions with Poisson noises Revised proofs and new theorems, such as explosive solutions of stochastic reaction diffusion equations Additional applications of stochastic PDEs to population biology and finance Updated section on parabolic equations and related elliptic problems in Gauss–Sobolev spaces The book covers basic theory as well as computational and analytical techniques to solve physical, biological, and financial problems. It first presents classical concrete problems before proceeding to a unified theory of stochastic evolution equations and describing applications, such as turbulence in fluid dynamics, a spatial population growth model in a random environment, and a stochastic model in bond market theory. The author also explores the connection of stochastic PDEs to infinite-dimensional stochastic analysis.
Almost Periodic Stochastic Processes
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Author : Paul H. Bezandry
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-07
Almost Periodic Stochastic Processes written by Paul H. Bezandry 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 2011-04-07 with Mathematics categories.
This book lays the foundations for a theory on almost periodic stochastic processes and their applications to various stochastic differential equations, functional differential equations with delay, partial differential equations, and difference equations. It is in part a sequel of authors recent work on almost periodic stochastic difference and differential equations and has the particularity to be the first book that is entirely devoted to almost periodic random processes and their applications. The topics treated in it range from existence, uniqueness, and stability of solutions for abstract stochastic difference and differential equations.
Asymptotic Analysis For Functional Stochastic Differential Equations
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Author : Jianhai Bao
language : en
Publisher: Springer
Release Date : 2016-11-19
Asymptotic Analysis For Functional Stochastic Differential Equations written by Jianhai Bao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-19 with Mathematics categories.
This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.