Stochastic Simulation: Algorithms and Analysis

ISBN-13: 9780387306797 / Angielski / Twarda / 2007 / 476 str.

Soren Asmussen; Peter W. Glynn

Opis

Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods, whereas the second half discusses model-specific algorithms. Given the wide range of examples, exercises and applications students, practitioners and researchers in probability, statistics, operations research, economics, finance, engineering as well as biology and chemistry and physics will find the book of value. Soren Asmussen is Professor of Applied Probability at Aarhus University, Denmark and Peter Glynn is Thomas Ford Professor of Engineering at Stanford University.

Recenzje

From the reviews:

"The adequate statistical simulation of random quantities is one of the challenges of this century. Therefore, sampling-based computational methods have become a fundamental part of the numerical toolset of both practitioners and researchers ... . This book provides a descriptive treatment of a variety of such sampling-based methods. Some steps to the mathematical analysis of their convergence properties and diverse applications are sketched as well. ... this book is of potential interest to many researchers, students and instructors." (Henri Schurz, Zentralblatt MATH, Vol. 1126 (3), 2008)

"This is a very interesting book for all who are interested in stochastic simulations. ... the book is designed as a potential teaching and learning tool for use in a wide variety of courses. ... it is a book that should be on the bookshelf of everybody who is seriously interested in stochastic simulations." (EMS Newsletter, September, 2008)

"The present book provides a broad treatment of sampling-based computational methods, as well as accompanying mathematical analysis of the convergence properties of these methods for a wide range of stochastic application problems. ... A set of exercises ... is also given at the end of each chapter. This book will be a reference of great value for researchers in probability, statistics, operations research, economics, finance, and engineering ... . It would also be perfect as a textbook for graduate seminars or courses in stochastic simulation." (Mou-Hsiung Chang, Siam Review, Vol. 51 (1), 2009)

"This book is intended to provide a broad treatment of the basic ideas and algorithms associated with sampling-based methods, often referred to as Monte Carlo algorithms or stochastic simulation. ... the book will be very useful to students and researchers from a wide range of disciplines." (John P. Lehoczky, Mathematical Reviews, Issue 2009 c)

"Stochastic Simulation, written by two prominent researchers in applied probability, is an outgrowth of that maturation. The authors' goal is not to tell the reader everything known about simulation, nor is it to give a collection of recipes, but rather to provide insight into analyzing problems via simulation. ... The book would make an excellent text for a graduate course in simulation, especially in a mathematical sciences department." (Peter C. Kiessler, Journal of the American Statistical Association, Vol. 104 (486), June, 2009)

Spis treści

General Methods and Algorithms.- Generating Random Objects.- Output Analysis.- Steady-State Simulation.- Variance-Reduction Methods.- Rare-Event Simulation.- Derivative Estimation.- Stochastic Optimization.- Algorithms for Special Models.- Numerical Integration.- Stochastic Di3erential Equations.- Gaussian Processes.- Lèvy Processes.- Markov Chain Monte Carlo Methods.- Selected Topics and Extended Examples.- What This Book Is About.- What This Book Is About.

Blurb

Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods, whereas the second half discusses model-specific algorithms.

Given the wide range of examples, exercises and applications students, practitioners and researchers in probability, statistics, operations research, economics, finance, engineering as well as biology and chemistry and physics will find the book of value.

Søren Asmussen is a professor of Applied Probability at Aarhus University, Denmark and Peter Glynn is the Thomas Ford professor of Engineering at Stanford University.