Markov processes and learning models, Volume 84 (Mathematics in Science and Engineering)

✍ Scribed by Norman (editor)

• Publisher: Academic Press
• Year: 1972
• Tongue: English
• Leaves: 289
• Edition: 1
• Category: Library

✦ Table of Contents

Front Cover
Markov Processes and Learning Models
Copyright Page
Contents
Preface
Chapter 0. Introduction
0.1 Experiments and Models
0.2 A General Theoretical Framework
0.3 Overview
PART I: DISTANCE DIMINISHING MODELS
Chapter 1. Markov Processes and Random Systems with Complete Connections
1.1 Markov Processes
1.2 Random Systems with Complete Connections
Chapter 2. Distance Diminishing Models and Doeblin–Fortet Processes
2.1 Distance Diminishing Models
2.2 Transition Operators for Metric State Spaces
Chapter 3. The Theorem of Ionescu Tulcea and Marinescu, and Compact Markov Processes
3.1 A Class of Operators
3.2 The Theorem of Ionescu Tulcea and Marinescu
3.3 Compact Markov Processes: Preliminaries
3.4 Ergodic Decomposition
3.5 Subergodic Decomposition
3.6 Regular and Absorbing Processes
3.7 Finite Markov Chains
Chapter 4. Distance Diminishing Models with Noncompact State Spaces
4.1 A Condition on p
4.2 Invariant Subsets
Chapter 5. Functions of Markov Processes
5.1 Introduction
5.2 Central Limit Theorem
5.3 Estimation of pu


5.6 Asymptotic Stationarity
5.7 Vector Valued Functions and Spectra
Chapter 6. Functions of Events
6.1 Theprocess Xn' = (En, Xn+1)
6.2 Unbounded Functions of Several Events
PART II: SLOW LEARNING
Chapter 7. Introduction to Slow Learning
7.1 Two Kinds of Slow Learning
7.2 Small Probability
7.3 Small Steps: Heuristics
Chapter 8. Transient Behavior in the Case of Large Drift
8.1 A General Central Limit Theorem
8.2 Properties of f(t)
8.3 Proofs of (A) and (B)
8.4 Proof of (C)
8.5 Near a Critical Point
Chapter 9. Transient Behavior in the Case of Small Drift
9.1 Diffusion Approximation in a Bounded Interval
9.2 Invariance
9.3 Semigroups
Chapter 10. Steady-State Behavior
10.1 A Limit Theorem for Stationary Probabilities
10.2 Proof of the Theorem

Chapter 11. Absorption Probabilities
11.1 Bounded State Spaces
11.2 Unbounded State Spaces
PART III: SPECIAL MODELS
Chapter 12. The Five–Operator Linear Model
12.1 Criteria for Regularity and Absorption
12.2 The Mean Learning Curve
12.3 Interresponse Dependencies
12.4 Slow Learning
Chapter 13. The Fixed Sample Size Model
13.1 Criteria for Regularity and Absorption
13.2 Mean Learning Curve and Interresponse Dependencies
13.3 Slow Learning
13.4 Convergence to the Linear Model
Chapter 14. Additive Models
14.1 Criteria for Recurrence and Absorption
14.2 Asymptotic A1 Response Frequency
14.3 Existence of Stationary Probabilities
14.4 Uniqueness of the Stationary Probability
14.5 Slow Learning
Chapter 15. Multiresponse Linear Models
15.1 Criteria for Regularity

Chapter 16. The Zeaman–House–Lovejoy Models
16.1 A Criterion for Absorption
16.2 Expected Total Errors
16.3 The Overlearning Reversal Effect
Chapter 17. Other Learning Models
17.1 Suppes’ Continuous Pattern Model
17.2 Successive Discrimination
17.3 Signal Detection: Forced-Choice
17.4 Signal Detection: Yes–No
Chapter 18. Diffusion Approximation in a Genetic Model and a Physical Model
18.1 Wright’s Model
18.2 The Ehrenfest Model
References
List of Symbols
Index