UID:
almatuudk_9922020381302884
Format:
1 online resource (xiii, 274 pages)
ISBN:
1-282-28974-8
,
9786612289743
,
0-08-095593-2
Series Statement:
Mathematics in science and engineering ; v. 84
Note:
Description based upon print version of record.
,
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
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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; 5.4 Estimation of s2; 5.5 A Representation of s2
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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
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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; 10.3 A More Precise Approximation to E(Xn?); 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
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13.1 Criteria for Regularity and Absorption13.2 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; 15.2 The Distribution of Yn and Y8; Chapter 16. The Zeaman-House-Lovejoy Models; 16.1 A Criterion for Absorption; 16.2 Expected Total Errors; 16.3 The Overlearning Reversal Effect
,
English
Additional Edition:
ISBN 0-12-521450-2
Language:
English
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