The Monte Carlo Method - 1st Edition - ISBN: 9780080110882, 9781483155579

The Monte Carlo Method

1st Edition

The Method of Statistical Trials

Editors: Yu.A. Shreider
eBook ISBN: 9781483155579
Imprint: Pergamon
Published Date: 1st January 1966
Page Count: 394
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The Monte Carlo Method: The Method of Statistical Trials is a systematic account of the fundamental concepts and techniques of the Monte Carlo method, together with its range of applications. Some of these applications include the computation of definite integrals, neutron physics, and in the investigation of servicing processes.
This volume is comprised of seven chapters and begins with an overview of the basic features of the Monte Carlo method and typical examples of its application to simple problems in computational mathematics. The next chapter examines the computation of multi-dimensional integrals using the Monte Carlo method. Some examples of statistical modeling of integrals are analyzed, together with the accuracy of the computations. Subsequent chapters focus on the applications of the Monte Carlo method in neutron physics; in the investigation of servicing processes; in communication theory; and in the generation of uniformly distributed random numbers on electronic computers. Methods for organizing statistical experiments on universal digital computers are discussed. This book is designed for a wide circle of readers, ranging from those who are interested in the fundamental applications of the Monte Carlo method, to those who are concerned with comparatively limited problems of the peculiarities of simulating physical processes.

Table of Contents

Preface to the English Edition


Chapter I. Principles of the Monte Carlo Method

§ 1. Definition, and Simple Examples of the Application, of the Monte Carlo Method

§ 2. Accuracy of the Monte Carlo Method, and its Principal Features

§ 3. Generation of Random Numbers

§ 4. Inversion of Matrices, and Solution of Systems of Linear Algebraic Equations

§ 5. The Random Walk Problem and the Solution of Boundary-value Problems

§ 6. The Monte Carlo Method and the Realization of Markov Processes on Computers

§ 7. Methods for Finding Eigenvalues and Eigenfunctions

§ 8. Specialized Machines for Solving Problems by the Monte Carlo Method

Chapter II. Computation of Definite Integrals

§ 1. Simple Examples of the Application of the Monte Carlo Method

§ 2. Some Methods for Reducing Variance

§ 3. Computation of Multi-dimensional Integrals

§ 4. On the Computation of Continual Integrals

§ 5. On the Application of Non-random Points within the Scheme of a Monte Carlo Method

Chapter III. Application of the Monte Carlo Method to Neutron Physics

§ 1. The Monte Carlo Method in Problems Concerning Elementary Particles

§ 2. Simple Collisions of Neutrons with Nuclei, and Their Simulation

§ 3. Transmission of Neutrons Through a Plate

§ 4. Some Methods for the Computation of Criticality of Nuclear Reactors

Chapter IV. Application of the Monte Carlo Method to the Investigation of Servicing Processes

§ 1. General Information about Servicing Problems

§ 2. Mathematical Description of the Arrival Flow of Requests for Servicing

§ 3. Servicing Systems

§ 4. Simulation of Random Arrival Flow of Requests

§ 5. Structure of an Algorithm for Solving Servicing Problems by the Monte Carlo Method

§ 6. Notes on Processing the Results of Simulations

Chapter V. Applications of the Monte Carlo Method to Communication Theory

§ 1. Statistical Properties of Signals and Noise

§ 2. Formulation of the Fundamental Problems of the Theory of Detection

§ 3. Methods for Solving Fundamental Problems of the Theory of Detection

§ 4. Other Problems

Chapter VI. Generation of Uniformly Distributed Random Variables on Electronic Computers

§ 1. Comparison of Various Methods of Generating Random Numbers

§ 2. Generation of Uniformly Distributed Pseudo-random Numbers on Electronic Computers

§ 3. Criteria for Testing the Quality of Uniformly Distributed Pseudorandom Numbers

§ 4. Physical Generation of Uniformly Distributed Random Variables

§ 5. Testing the Working of Random Number Devices

Chapter VII. Transformation of Random Numbers

§ 1. Properties of Quasi-uniform Variables

§ 2. Simulating Independent Random Events

§ 3. Characteristics of the Simulation of Events when Random Numbers with Few Digits are Used

§ 4. Techniques for Generating Random Numbers with a Specified Distribution Function

§ 5. Simulation of Random Vectors and Random Functions

§ 6. Simulating Certain Multi-dimensional Variables

§ 7. Simulation of Special Classes of Random Processes

Appendix I. Table of Random Digits

Appendix II. Table of Normal Variables



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About the Editor

Yu.A. Shreider

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