Stochastic Limit Theory: An Introduction for Econometricians

By James Davidson | Go to book overview
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Stochastic Limit Theory: An Introduction for Econometricians
Table of contents

Table of contents

  • Stochastic Limit Theory iii
  • Contents vii
  • Preface xiii
  • Acknowledgements xviii
  • Mathematical Symbols and Abbreviations xix
  • I - Mathematics 1
  • 1: Sets and Numbers 3
  • 2: Limits and Continuity 20
  • 3: Measure 36
  • 4: Integration 57
  • 5: Metric Spaces 75
  • 6: Topology 93
  • II - Probability 109
  • 7: Probability Spaces 111
  • 8: Random Variables 117
  • 9: Expectations 128
  • 10: Conditioning 143
  • 11: Characteristic Functions 161
  • III - Theory of Stochastic Processes 175
  • 12: Stochastic Processes 177
  • 13: Dependence 191
  • 14: Mixing 209
  • 15: Martingales 229
  • 16: Mixingales 247
  • 17: Near-Epoch Dependence 261
  • IV - The Law of Large Numbers 279
  • 18: Stochastic Convergence 281
  • 19: Convergence in Lp Norm 293
  • 20: The Strong Law of Large Numbers 306
  • 21: Uniform Stochastic Convergence 327
  • V - The Central Limit Theorem 345
  • 22: Weak Convergence of Distributions 347
  • 23: The Classical Central Limit Theorem 364
  • 24: Clts for Dependent Processes 380
  • 25: Some Extensions 399
  • VI - The Functional Central Limit Theorem 411
  • 26: Weak Convergence in Metric Spaces 413
  • 27: Weak Convergence in a Function Space 434
  • 28: Cadlag Functions 456
  • 29: Fclts for Dependent Variables 474
  • 30: Weak Convergence to Stochastic Integrals 496
  • References 519
  • Index 527
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