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Format: 1 online resource (227 p.)

ISBN: 1-282-30906-4 , 9786612309069 , 0-08-095526-6

Series Statement: Mathematics in science and engineering ; v. 20

Content: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Note: Description based upon print version of record. , Front Cover; Adaptive Processes in Economic Systems; Copyright Page; Contents; Preface; CHAPTER 1 Introduction; 1.1 The Historical and Current Development of Adaptive Theory; 1.2 Common Properties of Adaptive Processes; References; CHAPTER 2 The Mathematical Model; 2.1 Introduction; 2.2 Discrete Processes; 2.3 Some Discrete Sequential Processes; 2.4 The Role of the Decision Maker; 2.5 The Optimal Type 2 (Adaptive) Process; 2.6 The Constrained, Optimal Type 2 (Adaptive) Process; 2.7 Causality and Markov Processes; 2.8 The Dynamic Programming Model; References , CHAPTER 3 The Primitive Adaptive Process3.1 The Notion of Learning and Adaptation; 3.2 Some Hypothetical Experiments; 3.3 An Adaptive Process of the First Kind; 3.4 An Adaptive Process of the Second Kind; 3.5 Mixed Adaptive Processes of the First and Second Kind; 3.6 Summary; References; CHAPTER 4 Subjective Probability; 4.1 Introduction; 4.2 A Heuristic Example-The Three Investors; 4.3 Economic Environmental Processes; 4.4 A Digression on Statistical Estimators; 4.5 Multinomial Subjective Probabilities; 4.6Properties of the Subjective Probability Vector; References , CHAPTER 5 The Role of Entropy in Economic Processes5.1 The Concept of Entropy Time; 5.2Entropy and Information; 5.3The Entropy Paradox; References; CHAPTER 6 Adaptive Economic Processes; 6.1Introduction; 6.2General Deterministic Dynamic Economic Process; 6.3The Stochastic DynamicEconomic Process; 6.4The Adaptive Stochastic DynamicEconomic Process; 6.5Stochastic Growth Process; CHAPTER 7 An Adaptive Investment Model; 7.1The Objective Function; 7.2 An Example-The Three Investors Again; 7.3An Investment Model with Full Liquidity; 7.4An Adaptive Investment Process withFullLiquidity , 7.5Consideration of the Special Constraint7.6The Multivalued Payoff AdaptiveInvestmentProcess; References; CHAPTER 8 Multiactivity Capital Allocation Processes; 8.1Introduction; 8.2The Adaptive Capital Allocation Process; 8.3The Properties of the Adaptive CapitalAllocationProcess in the Limit; References; CHAPTER 9 Economic State Space; 9.1Introduction; 9.2The Concept of an Economic State Space; 9.3Statistical Equilibrium and Enlightenment; 9.4The Subjective Entropy Trajectory; 9.5The Dynamics of the SubjectiveEntropyTrajectory; 9.6The Economic State Space Representation , 9.7 A Digression-A Likely Value for the Environmental EntropyReferences; CHAPTER 10 Interactions between Decision Makers in State Space; 10.1 Introduction; 10.2 The State Space Probability Function; 10.3 Stochastic Equilibrium in the Market; 10.4 Interperson Trading in the Investment Market; CHAPTER 11 The Conclusions; 11.1 Individual Adaptive Behavior; 11.2 Collective Adaptive Behavior; Bibliography; 1. General Background on Adaptive and Evolutionary Behavior; 2. Sources on the Concept of Subjective Probability; 3. Sources on the Mathematical Theory of Intelligence , 4. Dynamic Programming and Adaptive Control , English

Additional Edition: ISBN 0-12-511350-1

Language: English

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Format: Online Ressource (xvi, 209 pages)

Edition: Reproduktion Online-Ausg. [S.l.] : HathiTrust Digital Library

ISBN: 0125113501 , 9780080955261 , 0080955266 , 9780125113502

Series Statement: Mathematics in science and engineering v. 20

Content: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Note: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002 , Online-Ausg. [S.l.] : HathiTrust Digital Library , Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.

Additional Edition: ISBN 9780125113502

Additional Edition: Erscheint auch als Druck-Ausgabe Murphy, Roy E Adaptive processes in economic systems New York, Academic Press, 1965

Language: English

Keywords: Electronic books

URL: Volltext

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