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Developed from the author’s course at the Ecole Polytechnique, Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear focuses on the simulation of stochastic processes in continuous time and their link with partial differential equations (PDEs). It covers linear and nonlinear problems in biology, finance, geophysics, mechanics, chemistry, and other application areas. The text also thoroughly develops the problem of numerical integration and computation of expectation by the Monte-Carlo method. The book begins with a history of Monte-Carlo methods and an overview of three typical Monte-Carlo problems: numerical integration and computation of expectation, simulation of complex distributions, and stochastic optimization. The remainder of the text is organized in three parts of progressive difficulty. The first part presents basic tools for stochastic simulation and analysis of algorithm convergence. The second part describes Monte-Carlo methods for the simulation of stochastic differential equations. The final part discusses the simulation of non-linear dynamics.
Book Synopsis Monte-Carlo Methods and Stochastic Processes by : Emmanuel Gobet
Download or read book Monte-Carlo Methods and Stochastic Processes written by Emmanuel Gobet and published by CRC Press. This book was released on 2016-09-15 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from the author’s course at the Ecole Polytechnique, Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear focuses on the simulation of stochastic processes in continuous time and their link with partial differential equations (PDEs). It covers linear and nonlinear problems in biology, finance, geophysics, mechanics, chemistry, and other application areas. The text also thoroughly develops the problem of numerical integration and computation of expectation by the Monte-Carlo method. The book begins with a history of Monte-Carlo methods and an overview of three typical Monte-Carlo problems: numerical integration and computation of expectation, simulation of complex distributions, and stochastic optimization. The remainder of the text is organized in three parts of progressive difficulty. The first part presents basic tools for stochastic simulation and analysis of algorithm convergence. The second part describes Monte-Carlo methods for the simulation of stochastic differential equations. The final part discusses the simulation of non-linear dynamics.
In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.
Book Synopsis Stochastic Simulation and Monte Carlo Methods by : Carl Graham
Download or read book Stochastic Simulation and Monte Carlo Methods written by Carl Graham and published by Springer Science & Business Media. This book was released on 2013-07-16 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.
A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.
Book Synopsis Handbook of Monte Carlo Methods by : Dirk P. Kroese
Download or read book Handbook of Monte Carlo Methods written by Dirk P. Kroese and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.
From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis
Book Synopsis Monte Carlo Methods in Financial Engineering by : Paul Glasserman
Download or read book Monte Carlo Methods in Financial Engineering written by Paul Glasserman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis
This accessible new edition explores the major topics in Monte Carlo simulation that have arisen over the past 30 years and presents a sound foundation for problem solving Simulation and the Monte Carlo Method, Third Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the state-of-the-art theory, methods and applications that have emerged in Monte Carlo simulation since the publication of the classic First Edition over more than a quarter of a century ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo, variance reduction techniques such as importance (re-)sampling, and the transform likelihood ratio method, the score function method for sensitivity analysis, the stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization, the cross-entropy method for rare events estimation and combinatorial optimization, and application of Monte Carlo techniques for counting problems. An extensive range of exercises is provided at the end of each chapter, as well as a generous sampling of applied examples. The Third Edition features a new chapter on the highly versatile splitting method, with applications to rare-event estimation, counting, sampling, and optimization. A second new chapter introduces the stochastic enumeration method, which is a new fast sequential Monte Carlo method for tree search. In addition, the Third Edition features new material on: • Random number generation, including multiple-recursive generators and the Mersenne Twister • Simulation of Gaussian processes, Brownian motion, and diffusion processes • Multilevel Monte Carlo method • New enhancements of the cross-entropy (CE) method, including the “improved” CE method, which uses sampling from the zero-variance distribution to find the optimal importance sampling parameters • Over 100 algorithms in modern pseudo code with flow control • Over 25 new exercises Simulation and the Monte Carlo Method, Third Edition is an excellent text for upper-undergraduate and beginning graduate courses in stochastic simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method. Reuven Y. Rubinstein, DSc, was Professor Emeritus in the Faculty of Industrial Engineering and Management at Technion-Israel Institute of Technology. He served as a consultant at numerous large-scale organizations, such as IBM, Motorola, and NEC. The author of over 100 articles and six books, Dr. Rubinstein was also the inventor of the popular score-function method in simulation analysis and generic cross-entropy methods for combinatorial optimization and counting. Dirk P. Kroese, PhD, is a Professor of Mathematics and Statistics in the School of Mathematics and Physics of The University of Queensland, Australia. He has published over 100 articles and four books in a wide range of areas in applied probability and statistics, including Monte Carlo methods, cross-entropy, randomized algorithms, tele-traffic c theory, reliability, computational statistics, applied probability, and stochastic modeling.
Book Synopsis Simulation and the Monte Carlo Method by : Reuven Y. Rubinstein
Download or read book Simulation and the Monte Carlo Method written by Reuven Y. Rubinstein and published by John Wiley & Sons. This book was released on 2016-10-21 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible new edition explores the major topics in Monte Carlo simulation that have arisen over the past 30 years and presents a sound foundation for problem solving Simulation and the Monte Carlo Method, Third Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the state-of-the-art theory, methods and applications that have emerged in Monte Carlo simulation since the publication of the classic First Edition over more than a quarter of a century ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo, variance reduction techniques such as importance (re-)sampling, and the transform likelihood ratio method, the score function method for sensitivity analysis, the stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization, the cross-entropy method for rare events estimation and combinatorial optimization, and application of Monte Carlo techniques for counting problems. An extensive range of exercises is provided at the end of each chapter, as well as a generous sampling of applied examples. The Third Edition features a new chapter on the highly versatile splitting method, with applications to rare-event estimation, counting, sampling, and optimization. A second new chapter introduces the stochastic enumeration method, which is a new fast sequential Monte Carlo method for tree search. In addition, the Third Edition features new material on: • Random number generation, including multiple-recursive generators and the Mersenne Twister • Simulation of Gaussian processes, Brownian motion, and diffusion processes • Multilevel Monte Carlo method • New enhancements of the cross-entropy (CE) method, including the “improved” CE method, which uses sampling from the zero-variance distribution to find the optimal importance sampling parameters • Over 100 algorithms in modern pseudo code with flow control • Over 25 new exercises Simulation and the Monte Carlo Method, Third Edition is an excellent text for upper-undergraduate and beginning graduate courses in stochastic simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method. Reuven Y. Rubinstein, DSc, was Professor Emeritus in the Faculty of Industrial Engineering and Management at Technion-Israel Institute of Technology. He served as a consultant at numerous large-scale organizations, such as IBM, Motorola, and NEC. The author of over 100 articles and six books, Dr. Rubinstein was also the inventor of the popular score-function method in simulation analysis and generic cross-entropy methods for combinatorial optimization and counting. Dirk P. Kroese, PhD, is a Professor of Mathematics and Statistics in the School of Mathematics and Physics of The University of Queensland, Australia. He has published over 100 articles and four books in a wide range of areas in applied probability and statistics, including Monte Carlo methods, cross-entropy, randomized algorithms, tele-traffic c theory, reliability, computational statistics, applied probability, and stochastic modeling.
This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrödinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.
Book Synopsis Monte Carlo Methods by : Malvin H. Kalos
Download or read book Monte Carlo Methods written by Malvin H. Kalos and published by John Wiley & Sons. This book was released on 2009-06-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrödinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.
This book provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide spectrum of engineering and scientific problems. It contains standard material usually considered in Monte Carlo simulation as well as new material such as variance reduction techniques, regenerative simulation, and Monte Carlo optimization.
Book Synopsis Simulation and the Monte Carlo Method by : Reuven Y. Rubinstein
Download or read book Simulation and the Monte Carlo Method written by Reuven Y. Rubinstein and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide spectrum of engineering and scientific problems. It contains standard material usually considered in Monte Carlo simulation as well as new material such as variance reduction techniques, regenerative simulation, and Monte Carlo optimization.
Gives greater rigor to numerical treatments of stochastic models. Contains Monte Carlo and quasi-Monte Carlo techniques, simulation of major stochastic procedures, deterministic methods adapted to Markovian problems and special problems related to stochastic integral and differential equations. Simulation methods are given throughout the text as well as numerous exercises.
Book Synopsis Numerical Methods for Stochastic Processes by : Nicolas Bouleau
Download or read book Numerical Methods for Stochastic Processes written by Nicolas Bouleau and published by John Wiley & Sons. This book was released on 1994-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives greater rigor to numerical treatments of stochastic models. Contains Monte Carlo and quasi-Monte Carlo techniques, simulation of major stochastic procedures, deterministic methods adapted to Markovian problems and special problems related to stochastic integral and differential equations. Simulation methods are given throughout the text as well as numerous exercises.
This text is concerned with a probabilistic approach to image analysis as initiated by U. GRENANDER, D. and S. GEMAN, B.R. HUNT and many others, and developed and popularized by D. and S. GEMAN in a paper from 1984. It formally adopts the Bayesian paradigm and therefore is referred to as 'Bayesian Image Analysis'. There has been considerable and still growing interest in prior models and, in particular, in discrete Markov random field methods. Whereas image analysis is replete with ad hoc techniques, Bayesian image analysis provides a general framework encompassing various problems from imaging. Among those are such 'classical' applications like restoration, edge detection, texture discrimination, motion analysis and tomographic reconstruction. The subject is rapidly developing and in the near future is likely to deal with high-level applications like object recognition. Fascinating experiments by Y. CHOW, U. GRENANDER and D.M. KEENAN (1987), (1990) strongly support this belief.
Book Synopsis Image Analysis, Random Fields and Dynamic Monte Carlo Methods by : Gerhard Winkler
Download or read book Image Analysis, Random Fields and Dynamic Monte Carlo Methods written by Gerhard Winkler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is concerned with a probabilistic approach to image analysis as initiated by U. GRENANDER, D. and S. GEMAN, B.R. HUNT and many others, and developed and popularized by D. and S. GEMAN in a paper from 1984. It formally adopts the Bayesian paradigm and therefore is referred to as 'Bayesian Image Analysis'. There has been considerable and still growing interest in prior models and, in particular, in discrete Markov random field methods. Whereas image analysis is replete with ad hoc techniques, Bayesian image analysis provides a general framework encompassing various problems from imaging. Among those are such 'classical' applications like restoration, edge detection, texture discrimination, motion analysis and tomographic reconstruction. The subject is rapidly developing and in the near future is likely to deal with high-level applications like object recognition. Fascinating experiments by Y. CHOW, U. GRENANDER and D.M. KEENAN (1987), (1990) strongly support this belief.
This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
Book Synopsis Backward Stochastic Differential Equations by : N El Karoui
Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
