## Stationary Processes and Prediction TheoryThe description for this book, Stationary Processes and Prediction Theory. (AM-44), Volume 44, will be forthcoming. |

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### Contents

INTRODUCTION | 1 |

STOCHASTIC PROCESSES AND STOCHASTIC SEQUENCES | 8 |

THE PREDICTION PROBLEMS FOR SEQUENCES | 56 |

EXAMPLES AND COUNTEREXAMPLES | 75 |

CHAPTER U SUBPROCESSES OF MARKOFF PROCESSES | 88 |

17 Normality and Continuous Predictability | 102 |

CHAPTER 5 STOCHASTIC SEMIGROUPS AND CONTINUOUS PREDICTABILITY | 110 |

STATISTICAL PREDICTABILITY | 130 |

2U Applications to Finite Dimensional Processes | 145 |

CHAPTER 7 INDUCTIVE FUNCTIONS | 152 |

26 GroupValued Inductive Functions | 165 |

27 Periodic Subsequences of Regular Sequences | 172 |

INDUCTIVE FUNCTIONS AND MARKOFF PROCESSES | 181 |

PROJECTIVE INDUCTIVE FUNCTIONS AND PREDICTION | 207 |

BIBLIOGRAPHY | 282 |

23 The Continuously Predictable Cover of a Finitely | 138 |

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### Common terms and phrases

A-sequence adjoint algebra closed set completes the proof components composite process condition cone consider continuous functions continuously predictable converges corollary corresponding defined definition denote dense dense set derived sequence determined E-algebra element equidistributed ergodic solution exists finite state Markoff follows functional equation Hausdorff space Hence homomorphism identical implies inductive function integers L-extension L-sequence left-infinite sequence Lemma limit process m-Markoff Markoff process Markoff sequence measurable functions metric Moreover non-negative periodic sequence positive probability predicting sequence prediction measure probability measure process X projective inductive function prove quence range regular sequence right-infinite sample sequence sample space satisfying stationary process statistically predictable stochastic semigroup stochastic sequence subalgebra subprocess subset suppose theorem topologically ergodic transformation transition probabilities two-sided unique upper density values vanishes variables vector X-ergodic xn+1 zn+1