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Nonlinear Stochastic Evolution Problems In Applied Sciences
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Book Synopsis Nonlinear Stochastic Evolution Problems in Applied Sciences by : N. Bellomo
Download or read book Nonlinear Stochastic Evolution Problems in Applied Sciences written by N. Bellomo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the analysis of nonlinear evolution problems described by partial differential equations having random or stochastic parameters. The emphasis throughout is on the actual determination of solutions, rather than on proving the existence of solutions, although mathematical proofs are given when this is necessary from an applications point of view. The content is divided into six chapters. Chapter 1 gives a general presentation of mathematical models in continuum mechanics and a description of the way in which problems are formulated. Chapter 2 deals with the problem of the evolution of an unconstrained system having random space-dependent initial conditions, but which is governed by a deterministic evolution equation. Chapter 3 deals with the initial-boundary value problem for equations with random initial and boundary conditions as well as with random parameters where the randomness is modelled by stochastic separable processes. Chapter 4 is devoted to the initial-boundary value problem for models with additional noise, which obey Ito-type partial differential equations. Chapter 5 is essential devoted to the qualitative and quantitative analysis of the chaotic behaviour of systems in continuum physics. Chapter 6 provides indications on the solution of ill-posed and inverse problems of stochastic type and suggests guidelines for future research. The volume concludes with an Appendix which gives a brief presentation of the theory of stochastic processes. Examples, applications and case studies are given throughout the book and range from those involving simple stochasticity to stochastic illposed problems. For applied mathematicians, engineers and physicists whose work involves solving stochastic problems.
Book Synopsis Stochastic Evolution Systems by : Boris L. Rozovsky
Download or read book Stochastic Evolution Systems written by Boris L. Rozovsky and published by Springer. This book was released on 2018-10-03 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.
Book Synopsis High-dimensional Nonlinear Diffusion Stochastic Processes by : Yevgeny Mamontov
Download or read book High-dimensional Nonlinear Diffusion Stochastic Processes written by Yevgeny Mamontov and published by World Scientific. This book was released on 2001 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This book is one of the first few devoted to high-dimensional diffusion stochastic processes with nonlinear coefficients. These processes are closely associated with large systems of Ito's stochastic differential equations and with discretized-in-the-parameter versions of Ito's stochastic differential equations that are nonlocally dependent on the parameter. The latter models include Ito's stochastic integro-differential, partial differential and partial integro-differential equations.The book presents the new analytical treatment which can serve as the basis of a combined, analytical -- numerical approach to greater computational efficiency. Some examples of the modelling of noise in semiconductor devices are provided
Book Synopsis Discovering Evolution Equations with Applications by : Mark McKibben
Download or read book Discovering Evolution Equations with Applications written by Mark McKibben and published by CRC Press. This book was released on 2011-06-03 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis New developments in Functional and Fractional Differential Equations and in Lie Symmetry by : Ioannis P. Stavroulakis
Download or read book New developments in Functional and Fractional Differential Equations and in Lie Symmetry written by Ioannis P. Stavroulakis and published by MDPI. This book was released on 2021-09-03 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delay, difference, functional, fractional, and partial differential equations have many applications in science and engineering. In this Special Issue, 29 experts co-authored 10 papers dealing with these subjects. A summary of the main points of these papers follows: Several oscillation conditions for a first-order linear differential equation with non-monotone delay are established in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, whereas a sharp oscillation criterion using the notion of slowly varying functions is established in A Sharp Oscillation Criterion for a Linear Differential Equation with Variable Delay. The approximation of a linear autonomous differential equation with a small delay is considered in Approximation of a Linear Autonomous Differential Equation with Small Delay; the model of infection diseases by Marchuk is studied in Around the Model of Infection Disease: The Cauchy Matrix and Its Properties. Exact solutions to fractional-order Fokker–Planck equations are presented in New Exact Solutions and Conservation Laws to the Fractional-Order Fokker–Planck Equations, and a spectral collocation approach to solving a class of time-fractional stochastic heat equations driven by Brownian motion is constructed in A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise. A finite difference approximation method for a space fractional convection-diffusion model with variable coefficients is proposed in Finite Difference Approximation Method for a Space Fractional Convection–Diffusion Equation with Variable Coefficients; existence results for a nonlinear fractional difference equation with delay and impulses are established in On Nonlinear Fractional Difference Equation with Delay and Impulses. A complete Noether symmetry analysis of a generalized coupled Lane–Emden–Klein–Gordon–Fock system with central symmetry is provided in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, and new soliton solutions of a fractional Jaulent soliton Miodek system via symmetry analysis are presented in New Soliton Solutions of Fractional Jaulent-Miodek System with Symmetry Analysis.
Book Synopsis Asymptotic Theory of Nonlinear Regression by : A.A. Ivanov
Download or read book Asymptotic Theory of Nonlinear Regression written by A.A. Ivanov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let us assume that an observation Xi is a random variable (r.v.) with values in 1 1 (1R1 , 8 ) and distribution Pi (1R1 is the real line, and 8 is the cr-algebra of its Borel subsets). Let us also assume that the unknown distribution Pi belongs to a 1 certain parametric family {Pi() , () E e}. We call the triple £i = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment £n = {lRn, 8 , P; ,() E e} is the product of the statistical experiments £i, i = 1, ... ,n if PO' = P () X ... X P () (IRn 1 n n is the n-dimensional Euclidean space, and 8 is the cr-algebra of its Borel subsets). In this manner the experiment £n is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments £n generated by observations of the form j = 1, ... ,n. (0.1) Xj = g(j, (}) + cj, c c In (0.1) g(j, (}) is a non-random function defined on e , where e is the closure in IRq of the open set e ~ IRq, and C j are independent r. v .-s with common distribution function (dJ.) P not depending on ().
Book Synopsis Random Fields and Stochastic Partial Differential Equations by : Y. Rozanov
Download or read book Random Fields and Stochastic Partial Differential Equations written by Y. Rozanov and published by Springer Science & Business Media. This book was released on 1998-03-31 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers some models described by means of partial dif ferential equations and boundary conditions with chaotic stochastic disturbance. In a framework of stochastic Partial Differential Equa tions an approach is suggested to generalize solutions of stochastic Boundary Problems. The main topic concerns probabilistic aspects with applications to well-known Random Fields models which are representative for the corresponding stochastic Sobolev spaces. {The term "stochastic" in general indicates involvement of appropriate random elements. ) It assumes certain knowledge in general Analysis and Probability {Hilbert space methods, Schwartz distributions, Fourier transform) . I A very general description of the main problems considered can be given as follows. Suppose, we are considering a random field ~ in a region T ~ Rd which is associated with a chaotic (stochastic) source"' by means of the differential equation (*) in T. A typical chaotic source can be represented by an appropri ate random field"' with independent values, i. e. , generalized random function"' = ( cp, 'TJ), cp E C~(T), with independent random variables ( cp, 'fJ) for any test functions cp with disjoint supports. The property of having independent values implies a certain "roughness" of the ran dom field "' which can only be treated functionally as a very irregular Schwarz distribution. With the lack of a proper development of non linear analyses for generalized functions, let us limit ourselves to the 1 For related material see, for example, J. L. Lions, E.
Book Synopsis Stochastic Processes: General Theory by : Malempati M. Rao
Download or read book Stochastic Processes: General Theory written by Malempati M. Rao and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role: a unique feature of the book. Applications to higher order stochastic differential equations and their special features are presented in detail. Stochastic processes in a manifold and multiparameter stochastic analysis are also discussed. Each of the seven chapters includes complements, exercises and extensive references: many avenues of research are suggested. The book is a completely revised and enlarged version of the author's Stochastic Processes and Integration (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material. Audience: Suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.
Book Synopsis Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control by : N. U. Ahmed
Download or read book Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control written by N. U. Ahmed and published by Springer Nature. This book was released on 2023-09-12 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach. The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature. This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.
Book Synopsis Limit Theorems for Random Fields with Singular Spectrum by : Nikolai Leonenko
Download or read book Limit Theorems for Random Fields with Singular Spectrum written by Nikolai Leonenko and published by Springer Science & Business Media. This book was released on 1999-02-28 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents limit theorems for nonlinear functionals of random fields with singular spectrum on the basis of various asymptotic expansions. This book will be of interest to mathematicians who use random fields in engineering or other applications.
Author :Vladimir V. Kalashnikov Publisher :Springer Science & Business Media ISBN 13 :9401716935 Total Pages :285 pages Book Rating :4.4/5 (17 download)
Book Synopsis Geometric Sums: Bounds for Rare Events with Applications by : Vladimir V. Kalashnikov
Download or read book Geometric Sums: Bounds for Rare Events with Applications written by Vladimir V. Kalashnikov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews problems associated with rare events arising in a wide range of circumstances, treating such topics as how to evaluate the probability an insurance company will be bankrupted, the lifetime of a redundant system, and the waiting time in a queue. Well-grounded, unique mathematical evaluation methods of basic probability characteristics concerned with rare events are presented, which can be employed in real applications, as the volume also contains relevant numerical and Monte Carlo methods. The various examples, tables, figures and algorithms will also be appreciated. Audience: This work will be useful to graduate students, researchers and specialists interested in applied probability, simulation and operations research.
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.
Book Synopsis Asymptotic Behaviour of Linearly Transformed Sums of Random Variables by : V.V. Buldygin
Download or read book Asymptotic Behaviour of Linearly Transformed Sums of Random Variables written by V.V. Buldygin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop erties of almost all sample paths of the sequences involved (strong limit theorems). Although either of these directions is closely related to another one, each of them has its own range of specific problems, as well as the own methodology for solving the underlying problems. This book is devoted to the second of the above mentioned lines, which means that we study asymptotic behaviour of almost all sample paths of linearly transformed sums of independent random variables, vectors, and elements taking values in topological vector spaces. In the classical works of P.Levy, A.Ya.Khintchine, A.N.Kolmogorov, P.Hartman, A.Wintner, W.Feller, Yu.V.Prokhorov, and M.Loeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari ables was constructed. This theory not only provides conditions of the almost sure convergence of series of independent random variables, but also studies different ver sions of the strong law of large numbers and the law of the iterated logarithm. One should point out that, even in this traditional framework, there are still problems which remain open, while many definitive results have been obtained quite recently.
Book Synopsis Unimodality of Probability Measures by : Emile M.J. Bertin
Download or read book Unimodality of Probability Measures written by Emile M.J. Bertin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this monograph is Khinchin-type representation theorems. An abstract framework for unimodality, an example of applied functional analysis, is developed for the introduction of different types of unimodality and the study of their behaviour. Also, several useful consequences or ramifications tied to these notions are provided. Being neither an encyclopaedia, nor a historical overview, this book aims to serve as an understanding of the basic features of unimodality. Chapter 1 lays a foundation for the mathematical reasoning in the chapters following. Chapter 2 deals with the concept of Khinchin space, which leads to the introduction of beta-unimodality in Chapter 3. A discussion on several existing multivariate notions of unimodality concludes this chapter. Chapter 4 concerns Khinchin's classical unimodality, and Chapter 5 is devoted to discrete unimodality. Chapters 6 and 7 treat the concept of strong unimodality on R and to Ibragimov-type results characterising the probability measures which preserve unimodality by convolution, and the concept of slantedness, respectively. Most chapters end with comments, referring to historical aspects or supplying complementary information and open questions. A practical bibliography, as well as symbol, name and subject indices ensure efficient use of this volume. Audience: Both researchers and applied mathematicians in the field of unimodality will value this monograph, and it may be used in graduate courses or seminars on this subject too.
Book Synopsis Evaluation of the Built Environment for Sustainability by : Vicenzo Bentivegna
Download or read book Evaluation of the Built Environment for Sustainability written by Vicenzo Bentivegna and published by Taylor & Francis. This book was released on 2003-09-02 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sustainability in the built environment is a major issue facing policy-makers, planners, developers and designers in the UK, Europe and worldwide. The measuring of buildings and cities for sustainability becomes increasingly important as pressure for green, sustainable development translates into policy and legislation. The problems of such measurement and evaluation are presented by the authors in contributions which move from the general to the particular, e.g. from a general framework for an environmentally sustainable form of urban development to a specific input-output model application to environmental problems. The book is divided into three parts: the first covers city models and sustainable systems - research programmes, environmental policies, green corporations and collaborative strategies to make urban development more sustainable; part two discusses the problems of evaluating the built environment in planning and construction, covering economic and environmental methods and construction, development and regeneration processes; part three illustrates a number of applications using different approaches and techniques and referring to a range of environmental aspects of the natural and built environment, from maintaining historic buildings to transport management and air pollution monitoring.
Book Synopsis Limit Theory for Mixing Dependent Random Variables by : Lin Zhengyan
Download or read book Limit Theory for Mixing Dependent Random Variables written by Lin Zhengyan and published by Springer Science & Business Media. This book was released on 1997-07-31 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: For many practical problems, observations are not independent. In this book, limit behaviour of an important kind of dependent random variables, the so-called mixing random variables, is studied. Many profound results are given, which cover recent developments in this subject, such as basic properties of mixing variables, powerful probability and moment inequalities, weak convergence and strong convergence (approximation), limit behaviour of some statistics with a mixing sample, and many useful tools are provided. Audience: This volume will be of interest to researchers and graduate students in the field of probability and statistics, whose work involves dependent data (variables).
Book Synopsis Probability Theory, Random Processes and Mathematical Statistics by : Y. Rozanov
Download or read book Probability Theory, Random Processes and Mathematical Statistics written by Y. Rozanov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability Theory, Theory of Random Processes and Mathematical Statistics are important areas of modern mathematics and its applications. They develop rigorous models for a proper treatment for various 'random' phenomena which we encounter in the real world. They provide us with numerous tools for an analysis, prediction and, ultimately, control of random phenomena. Statistics itself helps with choice of a proper mathematical model (e.g., by estimation of unknown parameters) on the basis of statistical data collected by observations. This volume is intended to be a concise textbook for a graduate level course, with carefully selected topics representing the most important areas of modern Probability, Random Processes and Statistics. The first part (Ch. 1-3) can serve as a self-contained, elementary introduction to Probability, Random Processes and Statistics. It contains a number of relatively sim ple and typical examples of random phenomena which allow a natural introduction of general structures and methods. Only knowledge of elements of real/complex analysis, linear algebra and ordinary differential equations is required here. The second part (Ch. 4-6) provides a foundation of Stochastic Analysis, gives information on basic models of random processes and tools to study them. Here a familiarity with elements of functional analysis is necessary. Our intention to make this course fast-moving made it necessary to present important material in a form of examples.
