Verfügbarkeit: Stochastic limit theory :: Universität Regensburg

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Titel:	Stochastic limit theory an introduction for econometricians
Von:	James Davidson
Person:	Davidson, James E. H. 1944- Verfasser aut
Hauptverfasser:	Davidson, James E. H. 1944- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Oxford Oxford University Press 2021
Ausgabe:	Second edition
Notation:	QH 237 QH 300 SK 800 SK 845
Schlagwörter:	Econometrics Limit theorems (Probability theory) Stochastic processes Martingal Ökonometrie Stochastik Stochastische Konvergenz Grenzwertsatz Stochastisches Integral Zentraler Grenzwertsatz
Medienzugang:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033036597&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	xxix, 777 Seiten Illustrationen
ISBN:	9780192844507

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adam_text	Contents From Preface to the First Edition Preface to the Second Edition Mathematical Symbols and Abbreviations xvii xxi xxv I. MATHEMATICS 1. Sets and Numbers 1.1 Basic Set Theory 1.2 Mappings 1.3 Countable Sets 1.4 The Real Continuum 1.5 Sequences of Sets 1.6 Classes of Subsets 1.7 Sigma Fields 1.8 The Topology of the Real Line 3 3 6 9 11 14 15 18 22 2. Limits, Sequences, and Sums 2.1 Sequences and Limits 2.2 Functions and Continuity 2.3 Vector Sequences and Functions 2.4 Sequences of Functions 2.5 Summability and Order Relations 2.6 Inequalities 2.7 Regular Variation 2.8 Arrays 28 28 32 35 37 37 41 45 48 3. Measure 3.1 Measure Spaces 3.2 The Extension Theorem 3.3 Non-measurability 3.4 Product Spaces 3.5 Measurable Transformations 3.6 Borei Functions 51 51 57 65 68 70 77 4. Integration 4.1 Construction of the Integral 4.2 Properties of the Integral 4.3 Product Measure and Multiple Integrals 4.4 The Radon-Nikodym Theorem 80 80 85 90 96 X CONTENTS 5. Metric Spaces 5.1 Spaces 5.2 Distances and Metrics 5.3 Separability and Completeness 5.4 Examples 5.5 Mappings on Metric Spaces 5.6 Function Spaces 103 103 104 108 112 115 119 6. Topology 6.1 Topological Spaces 6.2 Countability and Compactness 6.3 Separation Properties 6.4 Weak Topologies 6.5 The Topology of Product Spaces 6.6 Embedding and Metrization 126 126 128 132 135 136 140 II. PROBABILITY 7. Probability Spaces 7.1 Probability Measures 7.2 Conditional Probability 7.3 Independence 7.4 Product Spaces 147 147 149 151 153 8. Random Variables 8.1 Measures on the Line 8.2 Distribution Functions 8.3 Examples 8.4 Multivariate Distributions 8.5 Independent Random Variables 154 154 155 160 166 169 9. Expectations 9.1 Averages and Integrals 9.2 Applications 9.3 Expectations of Functions of X 9.4 Moments 9.5 Theorems for the Probabilist’s Toolbox 9.6 Multivariate Distributions 9.7 More Theorems for the Toolbox 9.8 Random Variables Depending on a Parameter 171 171 172 174 176 178 182 185 188 10. Conditioning 10.1 Conditioning in Product Measures 10.2 Conditioning on a Sigma Field 10.3 Conditional Expectations 190 190 193 195 CONTENTS 10.4 Some Theorems on Conditional Expectations 10.5 Relationships between Sub-a-fields 10.6 Conditional Distributions 11. Characteristic Functions 11.1 The Distribution of Sums of Random Variables 11.2 Complex Numbers 11.3 The Theory of Characteristic Functions 11.4 Examples 11.5 Infinite Divisibility 11.6 The Inversion Theorem 11.7 The Conditional Characteristic Function XX 197 204 208 213 213 215 218 221 223 227 230 III. THEORY OF STOCHASTIC PROCESSES 12. Stochastic Processes 12.1 Basic Ideas and Terminology 12.2 Convergence of Stochastic Sequences 12.3 The Probability Model 12.4 The Consistency Theorem 12.5 Uniform and Limiting Properties 12.6 Uniform Integrability 237 237 238 239 244 247 249 13. Time Series Models 13.1 Independence and Stationarity 13.2 The Poisson Process 13.3 Linear Processes 13.4 Random Walks 255 255 259 261 267 14. Dependence 14.1 Shift Transformations 14.2 Invariant Events 14.3 Ergodicity and Mixing 14.4 Sub-a-fields and Regularity 14.5 Strong and Uniform Mixing 271 271 272 278 284 287 15. Mixing 15.1 Mixing Sequences of Random Variables 15.2 Mixing Inequalities 15.3 Mixing in Linear Processes 15.4 Sufficient Conditions for Strong and Uniform Mixing 290 290 292 297 301 16. Martingales 16.1 Sequential Conditioning 16.2 Extensions of the Martingale Concept 16.3 Martingale Convergence 313 313 319 322 ХІІ CONTENTS 16.4 Convergence and the Conditional Variances 16.5 Martingale Inequalities 328 330 17. Mixingales 17.1 Definition and Examples 17.2 Telescoping Sum Representations 17.3 Maximal Inequalities 17.4 Uniform Square-Integrability 17.5 Autocovariances 344 344 347 351 357 361 18. Near-Epoch Dependence 18.1 Definitions and Examples 18.2 Near-Epoch Dependence and Mixingales 18.3 Transformations 18.4 Adaptation 18.5 Approximability 18.6 NED in Volatility 368 368 373 375 383 387 392 IV. THE LAW OF LARGE NUMBERS 19. Stochastic Convergence 19.1 Almost Sure Convergence 19.2 Convergence in Probability 19.3 Transformations and Convergence 19.4 Convergence in Lp Norm 19.5 Examples 19.6 Laws of Large Numbers 401 401 405 406 411 412 413 20. Convergence in Lp Norm 20.1 Weak Laws by Mean Square Convergence 20.2 Almost Sure Convergence by the Method of Subsequences 20.3 Truncation Arguments 20.4 A Martingale Weak Law 20.5 Mixingale Weak Laws 20.6 Approximable Processes 418 418 422 426 427 432 435 21. The Strong Law of Large Numbers 21.1 Technical Tricks for Proving LLNs 21.2 The Case of Independence 21.3 Martingale Strong Laws 21.4 Conditional Variances and Random Weighting 21.5 Strong Laws for Mixingales 21.6 NED and Mixing Processes 438 438 443 449 452 455 468 CONTENTS 22. Uniform Stochastic Convergence 22.1 Stochastic Functions on a Parameter Space 22.2 Pointwise and Uniform Convergence 22.3 Stochastic Equicontinuity 22.4 Generic Uniform Convergence 22.5 Uniform Laws of Large Numbers ХІІІ 471 471 475 480 482 486 V. THE CENTRAL LIMIT THEOREM 23. Weak Convergence of Distributions 23.1 Basic Concepts 23.2 The Skorokhod Representation Theorem 23.3 Weak Convergence and Transformations 23.4 Convergence of Moments and Characteristic Functions 23.5 Criteria for Weak Convergence 23.6 Convergence of Random Sums 23.7 Stable Distributions 495 495 498 504 506 509 512 514 24. The Classical Central Limit Theorem 24.1 The I.I.D. Case 24.2 Independent Heterogeneous Sequences 24.3 Feller’s Theorem and Asymptotic Negligibility 24.4 The Case of Trending Variances 24.5 Gaussianity by Other Means 24.6 a-Stable Convergence 520 520 525 531 535 537 542 25. CLTs for Dependent Processes 25.1 A General Convergence Theorem 25.2 The Martingale Case 25.3 Stationary Ergodic Sequences 25.4 The CLT for Mixingales 25.5 NED Functions of Mixing Processes 548 548 551 553 555 563 26. Extensions and Complements 26.1 The CLT with Estimated Normalization 26.2 The CLT for Linear Processes 26.3 The CLT with Random Norming 26.4 The Multivariate CLT 26.5 The Delta Method 26.6 Law of the Iterated Logarithm 26.7 Berry-Esséen Bounds 568 568 576 577 580 583 586 590 xiv CONTENTS VI. THE FUNCTIONAL CENTRAL LIMIT THEOREM 27. Measures on Metric Spaces 27.1 Separability and Measurability 27.2 Measures and Expectations 27.3 Function Spaces 27.4 The Space C 27.5 Measures on C 27.6 Wiener Measure 28. Stochastic Processes in Continuous Time 28.1 Adapted Processes 28.2 Diffusions and Martingales 28.3 Brownian Motion 28.4 Properties of Brownian Motion 28.5 Skorokhod Embedding 28.6 Processes Derived from Brownian Motion 28.7 Independent Increments and Continuity 29. Weak Convergence 29.1 Weak Convergence in Metric Spaces 29.2 Skorokhod’s Representation 29.3 Metrizing the Space of Measures 29.4 Tightness and Convergence 29.5 Weak Convergence in C 29.6 An FCLT for MartingaleDifferences 29.7 lhe Multivariate Case 30. Càdlàg Functions 30.1 The Space D 30.2 Metrizing D 30.3 Billingsley’s Metric 30.4 Measures on D 30.5 Prokhorov’s Metric 30.6 Compactness and Tightness in D 30.7 Weak Convergence in D 31. FCLTs for Dependent Variables 31.1 Asymptotic Independence 31.2 NED Functions of Mixing Processes 1 31.3 NED Functions of Mixing Processes 2 31.4 Nonstationary Increments 31.5 Generalized Partial Sums 31.6 The Multivariate Case 593 593 597 599 602 606 609 611 611 614 616 619 623 627 631 638 638 643 646 652 656 659 664 668 668 674 678 681 685 686 692 699 699 702 706 710 716 718 CONTENTS XV 32. Weak Convergence to Stochastic Integrals 32.1 Weak Limit Results for Random Functionals 32.2 Stochastic Integrals 32.3 Convergence to Stochastic Integrals 32.4 Convergence in Probability to Αχγ 724 724 728 737 747 Bibliography Index 757 767
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title	Stochastic limit theory an introduction for econometricians
title_auth	Stochastic limit theory an introduction for econometricians
title_exact_search	Stochastic limit theory an introduction for econometricians
title_full	Stochastic limit theory an introduction for econometricians James Davidson
title_fullStr	Stochastic limit theory an introduction for econometricians James Davidson
title_full_unstemmed	Stochastic limit theory an introduction for econometricians James Davidson
title_short	Stochastic limit theory
title_sort	stochastic limit theory an introduction for econometricians
title_sub	an introduction for econometricians
topic	Econometrics Limit theorems (Probability theory) Stochastic processes Martingal (DE-588)4126466-6 gnd Ökonometrie (DE-588)4132280-0 gnd Stochastik (DE-588)4121729-9 gnd Stochastische Konvergenz (DE-588)4183376-4 gnd Grenzwertsatz (DE-588)4158163-5 gnd Stochastisches Integral (DE-588)4126478-2 gnd Zentraler Grenzwertsatz (DE-588)4067618-3 gnd
topic_facet	Econometrics Limit theorems (Probability theory) Stochastic processes Martingal Ökonometrie Stochastik Stochastische Konvergenz Grenzwertsatz Stochastisches Integral Zentraler Grenzwertsatz
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033036597&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT davidsonjameseh stochasticlimittheoryanintroductionforeconometricians

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