Stationary Processes and Prediction Theory. (AM-44), Volume 44A classic treatment of stationary processes and prediction theory from the acclaimed Annals of Mathematics Studies series |
Contents
| 1 | |
CHAPTER 1 STOCHASTIC PROCESSES AND STOCHASTIC SEQUENCES | 8 |
CHAPTER 2 THE PREDICTION PROBLEMS FOR SEQUENCES | 56 |
CHAPTER 3 EXAMPLES AND COUNTEREXAMPLES | 75 |
CHAPTER 4 SUBPROCESSES OF MARKOFF PROCESSES | 88 |
CHAPTER 5 STOCHASTIC SEMIGROUPS AND CONTINUOUS PREDICTABILITY | 110 |
CHAPTER 6 STATISTICAL PREDICTABILITY | 130 |
CHAPTER 7 INDUCTIVE FUNCTIONS | 152 |
CHAPTER 8 INDUCTIVE FUNCTIONS AND MARKOFF PROCESSES | 181 |
CHAPTER 9 PROJECTIVE INDUCTIVE FUNCTIONS AND PREDICTION | 207 |
Other editions - View all
Stationary Processes and Prediction Theory. (AM-44), Volume 44 Harry Furstenberg No preview available - 1960 |
Common terms and phrases
A-sequence a₁ adjoint algebra andand bounded closed set compact completes the proof components composite process cone consider continuous functions continuously predictable converges corollary corresponding defined definition denote derived sequence determined E-algebra element equidistributed ergodic solution exists follows forfor functional equation Hausdorff space Hence homomorphism identical implies inductive function integers L-extension Lemma limit process linear m-Markoff Markoff process Markoff sequence metric non-negative ofof periodic sequence 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 statistical predictability stochastic semigroup stochastic sequence subprocess subset suppose thatthat theorem thethe topologically ergodic transformation transition probabilities two-sided unique upper density V₁ values vanishes variables vector w₁ Xn+1 Zn+1