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Author : Olga Fiedler
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (752 download)
Download or read book Weak Convergence of Approximate Solutions of Random Equations written by Olga Fiedler and published by . This book was released on 1992 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Heinz W. Engl
Publisher :
ISBN 13 :
Total Pages : 54 pages
Book Rating : 4.:/5 (255 download)
Download or read book Weak Convergence of Approximate Solutions of Stochastic Equations with Applications to Random Differential and Integral Equations written by Heinz W. Engl and published by . This book was released on 1985 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Amarjit Budhiraja
Publisher : Springer
ISBN 13 : 1493995790
Total Pages : 574 pages
Book Rating : 4.4/5 (939 download)
Download or read book Analysis and Approximation of Rare Events written by Amarjit Budhiraja and published by Springer. This book was released on 2019-08-10 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.
Author : Harold Joseph Kushner
Publisher : MIT Press
ISBN 13 : 9780262110907
Total Pages : 296 pages
Book Rating : 4.1/5 (19 download)
Download or read book Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory written by Harold Joseph Kushner and published by MIT Press. This book was released on 1984 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and methods for random processes and applies them to numerous problems of practical importance. In particular, it develops usable and broad conditions and techniques for showing that a sequence of processes converges to a Markov diffusion or jump process. This is useful when the natural physical model is quite complex, in which case a simpler approximation la diffusion process, for example) is usually made. The book simplifies and extends some important older methods and develops some powerful new ones applicable to a wide variety of limit and approximation problems. The theory of weak convergence of probability measures is introduced along with general and usable methods (for example, perturbed test function, martingale, and direct averaging) for proving tightness and weak convergence. Kushner's study begins with a systematic development of the method. It then treats dynamical system models that have state-dependent noise or nonsmooth dynamics. Perturbed Liapunov function methods are developed for stability studies of nonMarkovian problems and for the study of asymptotic distributions of non-Markovian systems. Three chapters are devoted to applications in control and communication theory (for example, phase-locked loops and adoptive filters). Smallnoise problems and an introduction to the theory of large deviations and applications conclude the book. Harold J. Kushner is Professor of Applied Mathematics and Engineering at Brown University and is one of the leading researchers in the area of stochastic processes concerned with analysis and synthesis in control and communications theory. This book is the sixth in The MIT Press Series in Signal Processing, Optimization, and Control, edited by Alan S. Willsky.
Author : Albert T. Bharucha-Reid
Publisher : North-Holland
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.:/5 (44 download)
Download or read book Approximate Solution of Random Equations written by Albert T. Bharucha-Reid and published by North-Holland. This book was released on 1979 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Raphael Kruse
Publisher : Springer
ISBN 13 : 3319022318
Total Pages : 188 pages
Book Rating : 4.3/5 (19 download)
Download or read book Strong and Weak Approximation of Semilinear Stochastic Evolution Equations written by Raphael Kruse and published by Springer. This book was released on 2013-11-18 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut’s integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq.
Author : Robert E. O'Malley
Publisher : SIAM
ISBN 13 : 9780898713022
Total Pages : 424 pages
Book Rating : 4.7/5 (13 download)
Download or read book ICIAM 91 written by Robert E. O'Malley and published by SIAM. This book was released on 1992-01-01 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings -- Computer Arithmetic, Algebra, OOP.
Author : Peter E. Kloeden
Publisher : Springer Science & Business Media
ISBN 13 : 3662126168
Total Pages : 666 pages
Book Rating : 4.6/5 (621 download)
Download or read book Numerical Solution of Stochastic Differential Equations written by Peter E. Kloeden and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP
Author : Harold Joseph Kushner
Publisher :
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (227 download)
Download or read book Asymptotic Distributions of Solutions of Ordinary Differential Equations with Wide Band Noise Inputs; Approximate Invariant Measures written by Harold Joseph Kushner and published by . This book was released on 1981 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let (x superscript epsilon (dot)) be a sequence of solutions to an ordinary differential equation with random right sides (due to input noise (xi superscript epsilon (dot)) and which converges weakly to a diffusion x(dot) with unique invariant measure mu(dot). Let mu(t, dot) denote the measure of x(t), and suppose that mu(t, dot) approaches mu (dot) weakly. The paper shows, under reasonable conditions, that the measures of x superscript epsilon (t) are close to mu (dot) for large t and small epsilon. In applications, such information is often more useful than the simple fact of the weak convergence. The noise xi superscript epsilon (dot) need not be bounded, the pair (x superscript epsilon (dot), xi(dot)) need not be Markovian (except for the unbounded noise case), and the dynamical terms need not be smooth. The discrete parameter case is treated, and several examples arising in control and communication theory are given.
Author : Eckhard Platen
Publisher : Springer Science & Business Media
ISBN 13 : 364213694X
Total Pages : 868 pages
Book Rating : 4.6/5 (421 download)
Download or read book Numerical Solution of Stochastic Differential Equations with Jumps in Finance written by Eckhard Platen and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt: In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.
Author : V. C. Joshua
Publisher : Springer Nature
ISBN 13 : 9811559511
Total Pages : 521 pages
Book Rating : 4.8/5 (115 download)
Download or read book Applied Probability and Stochastic Processes written by V. C. Joshua and published by Springer Nature. This book was released on 2020-08-29 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers selected papers presented at the International Conference on Advances in Applied Probability and Stochastic Processes, held at CMS College, Kerala, India, on 7–10 January 2019. It showcases high-quality research conducted in the field of applied probability and stochastic processes by focusing on techniques for the modelling and analysis of systems evolving with time. Further, it discusses the applications of stochastic modelling in queuing theory, reliability, inventory, financial mathematics, operations research, and more. This book is intended for a broad audience, ranging from researchers interested in applied probability, stochastic modelling with reference to queuing theory, inventory, and reliability, to those working in industries such as communication and computer networks, distributed information systems, next-generation communication systems, intelligent transportation networks, and financial markets.
Author : F. Angrand
Publisher : SIAM
ISBN 13 : 9780898712001
Total Pages : 524 pages
Book Rating : 4.7/5 (12 download)
Download or read book Numerical Methods for the Euler Equations of Fluid Dynamics written by F. Angrand and published by SIAM. This book was released on 1985-01-01 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jean-Luc Prigent
Publisher : Springer Science & Business Media
ISBN 13 : 3540248315
Total Pages : 432 pages
Book Rating : 4.5/5 (42 download)
Download or read book Weak Convergence of Financial Markets written by Jean-Luc Prigent and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. The main problems, which include portfolio optimization, option pricing and hedging are examined, especially when considering discrete-time approximations of continuous-time dynamics. The third part deals with lattice- and tree-based computational procedures for option pricing both on stocks and stochastic bonds. More general discrete approximations are also introduced and detailed. Includes detailed examples.
Author : Harold Kushner
Publisher : Springer Science & Business Media
ISBN 13 : 146124482X
Total Pages : 245 pages
Book Rating : 4.4/5 (612 download)
Download or read book Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).
Author : Simo Särkkä
Publisher : Cambridge University Press
ISBN 13 : 110869344X
Total Pages : 327 pages
Book Rating : 4.1/5 (86 download)
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-driven derivations and computational assignments. MATLAB/Octave source code is available for download, promoting hands-on work with the methods.
Author : John R. Birge
Publisher : Elsevier
ISBN 13 : 9780080553252
Total Pages : 1026 pages
Book Rating : 4.5/5 (532 download)
Download or read book Handbooks in Operations Research and Management Science: Financial Engineering written by John R. Birge and published by Elsevier. This book was released on 2007-11-16 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt: The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.
Author : Keith W. Hipel
Publisher : Springer Science & Business Media
ISBN 13 : 9401110727
Total Pages : 370 pages
Book Rating : 4.4/5 (11 download)
Download or read book Stochastic and Statistical Methods in Hydrology and Environmental Engineering written by Keith W. Hipel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Objectives The current global environmental crisis has reinforced the need for developing flexible mathematical models to obtain a better understanding of environmental problems so that effective remedial action can be taken. Because natural phenomena occurring in hydrology and environmental engineering usually behave in random and probabilistic fashions, stochastic and statistical models have major roles to play in the protection and restoration of our natural environment. Consequently, the main objective of this edited volume is to present some of the most up-to-date and promising approaches to stochastic and statistical modelling, especially with respect to groundwater and surface water applications. Contents As shown in the Table of Contents, the book is subdivided into the following main parts: GENERAL ISSUES PART I PART II GROUNDWATER PART III SURFACE WATER PART IV STOCHASTIC OPTIMIZATION PART V MOMENT ANALYSIS PART VI OTHER TOPICS Part I raises some thought-provoking issues about probabilistic modelling of hydro logical and environmental systems. The first two papers in Part I are, in fact, keynote papers delivered at an international environmetrics conference held at the University of Waterloo in June, 1993, in honour of Professor T. E. Unny. In his keynote pa per, Dr. S. J. Burges of the University of Washington places into perspective the historical and future roles of stochastic modelling in hydrology and environmental engineering. Additionally, Dr. Burges stresses the need for developing a sound scien tific basis for the field of hydrology. Professor P. E.
