A Contribution to the Theory of Stochastic Processes

Chapters in this book

1. Frontmatter I
2. PREFACE V
3. CONTENTS IX
4. [. Mathematical Statistics
5. Asymptotic Minimax Solutions of Sequential Point Estimation Problems 1
6. Some Applications of the Cramer-Rao Inequality 13
7. A Generalized T Test and Measure of Multivariate Dispersion 23
8. Tolerance Intervals for Linear Regression 43
9. Bayes and Minimax Estimates for Quadratic Loss Functions 53
10. Confidence Regions for Linear Regressions 75
11. "Optimum" Nonparametric Tests 83
12. Comparison of Experiments 93
13. The Asymptotic Distribution of Certain Characteristic Roots and Vectors 103
14. Asymptotically Subminimax Solutions of Compound Statistical Decision Problems 131
15. Characterization of the Minimal Complete Class of Decision Functions when the Number of Distributions and Decisions Is Finite 149
16. On Median Tests for Linear Hypotheses 159
17. Conditional Expectation and Convex Functions 167
18. II. Probability
19. Wiener's Random Function, and Other Laplacian Random Functions 171
20. On Some Connections between Probability Theory and Differential and Integral Equations 189
21. Recent Suggestions for the Reconciliation of Theories of Probability 217
22. Diffusion Processes in Genetics 227
23. Random Ergodic Theorems and Markoff Processes with a Stable Distribution 247
24. A Problem on Random Walk 263
25. Continuous Parameter Martingales 269
26. On Almost Sure Convergence 279
27. Some Mathematical Models for Branching Processes 305
28. A Contribution to the Theory of Stochastic Processes 329
29. The Strong Law of Large Numbers 341
30. Some Problems on Random Walk in Space 353
31. A Remark on Characteristic Functions 369
32. Random Functions from a Poisson Process 373
33. III. Astronomy
34. An Approach to the Dynamics of Stellar Systems 387
35. The Problem of Stellar Evolution Considered Statistically 403
36. Statistical Studies Relating to the Distribution of the Elements of Spectroscopic Binaries 417
37. Correction of Frequency Functions for Observational Errors of the Variables 437
38. Hydrodynamical Description of Stellar Motions 441
39. IV. Biometry
40. Improvement by Means of Selection 449
41. Relative Precision of Minimum Chi- Square and Maximum Likelihood Estimates of Regression Coefficients 471
42. V. Econometrics
43. Nonlinear Programming 481
44. Why "Should" Statisticians and Businessmen Maximize "Moral Expectation"? 493
45. An Extension of the Basic Theorems of Classical Welfare Economics 507
46. VI. Physics
47. The Concept of Probability in Quantum Mechanics 533
48. Statistical Questions in Meson Theory 543
49. Statistical Mechanics of a Continuous Medium (vibrating string with fixed ends) 553
50. Philosophical Problems of the Statistical Interpretation of Quantum Mechanics 567
51. Correlation of Position for the Ideal Quantum Gas 581
52. VII. Traffic Engineering
53. Distribution of Vehicle Speeds and Travel Times 589
54. Statistical Techniques in the Field of Traffic Engineering and Traffic Research 603
55. VIII. Wave Analysis
56. Correlograms for Pacific Ocean Waves 627
57. Experimental Correlogram Analyses of Artificial Time Series (with special reference to analyses of oceanographic data) 639