《Method of Statistical Testing MONTE CARLO METHOD》

CHAPTER Ⅰ．Fundamentals of the Monte Carlo Method1

1．Definition and Simple Examples of the Application of the Monte Carlo Method1

2．Accuracy of the Monte Carlo Method and its Main Characteristics7

3．Generation of Random Numbers13

4．Solution of Systems of Linear Algebraic Equations19

5．Random Walk and the Solution of Boundary Value Problems23

6．The Monte Carlo Method and the Simulation of Markov Processes in a Computer31

CHAPTER Ⅱ．Evaluation of Definite Integrals39

1．Simple Applications of the Monte Carlo Method39

2．Some Methods for Reducing the Variance46

3．Evaluation of Multidimensional Integrals61

4．Evaluation of Wiener Integrals73

5．Application of Quasi-Random Points to the Monte Carlo Scheme78

CHAPTER Ⅲ．Applications of the Monte Carlo Method in Neu-tron Physics84

1．The Monte Carlo Method in Elementary Particle Problems84

2．Simple Interactions of Neutrons With Nuclei and Their Simulation92

3．Passage of Neutrons Through a Plate104

4．Some Methods of Calculation of the Criticality of Nuclear Reactors118

CHAPTER Ⅳ．Application of the Monte Carlo Method to the Investigation of Mass Service or Congestion Processes,Including Queueing127

1．General Information on Mass-Service Problems127

2．Mathematical Description of an Input Consisting of a Stream of Calls Requiring Service129

3．Mass-Service Systems134

4．The Generation of Random Streams of Calls138

5．Structure of an Algorithm for Solving Mass-Service Problems by the Monte Carlo Method148

6．Considerations On the Processing of the Results of Simulation153

CHAPTER Ⅴ．Application of the Monte Carlo Method to Infor-mation Theory156

1．Statistical Properties of Signals and Noise156

2．Formulation of the Basic problems of Detection Theory170

3．procedure for the Solution of the Main problems of Detection Theory184

4．Other Problems188

CHAPTER Ⅵ．Generating Uniformly Distributed Random Quan-tities by Means of Electronic Computers196

1．Comparison of Various Methods of Generating Ran-dom Quantities196

2．Obtaining Uniform Pseudo-Random Numbers on Com-puters198

3．Criteria to Test the Quality of Uniform Pseudo-Random Numbers208

4．Physical Generators of Uniform Random Numbers220

5．Tests of the Operation of Random-Number gener-ators238

CHAPTER Ⅶ．Transformation of Random Numbers244

1．Properties of Quasi-Uniform Quantities244

2．Simulation of Independent Random Events247

3．Typical Features of the Simulation of Events by Means of Random Numbers With Few Digits251

4．Methods of Obtaining Random Numbers With Assigned Distribution Law252

5．Simulation of Random Vectors and Random Functions264

6．The Simulation of Certain Multidimensional Quan-tities266

APPENDICES273

REFERENCES281

INDEX299