Stationary Processes and Prediction TheoryA classic treatment of stationary processes and prediction theory from the acclaimed Annals of Mathematics Studies series |
Contents
INTRODUCTION | 1 |
7 Ergodic Properties of Regular Sequences | 7 |
SUBPROCESSES OF MARKOFF PROCESSES | 88 |
17 Normality and Continuous Predictability | 102 |
STOCHASTIC SEMIGROUPS AND CONTINUOUS PREDICTABILITY | 110 |
STATISTICAL PREDICTABILITY | 130 |
23 The Continuously Predictable Cover of a Finitely | 138 |
24 Applications to Finite Dimensional Processes | 145 |
3 | 160 |
Applications to Equidistribution | 171 |
Existence of Fourier Coefficients | 178 |
4 | 192 |
CHAPTER 3 | 205 |
32 Adjoint Processes | 241 |
BIBLIOGRAPHY | 282 |
CHAPTER 7 | 151 |
Other editions - View all
Stationary Processes and Prediction Theory. (AM-44), Volume 44 Harry Furstenberg No preview available - 1960 |
Stationary Processes and Prediction Theory. (AM-44), Volume 44 Harry Furstenberg No preview available - 1960 |
Common terms and phrases
A-sequence a₁ adjoint algebra c.p. cover completes the proof components composite process condition cone consider continuous functions continuously predictable converges corollary corresponding defined definition denote dense derived sequence determined E-algebra elements equidistributed ergodic solution exists extension follows functional equation G(YX Hausdorff space Hence homomorphism identical implies inductive function integers Ky(x L-extension left-infinite sequence Lemma m-Markoff Markoff process Markoff sequence metric Moreover non-negative possible sequence prediction measure probability measure process with transition process X prove quence random process range regular sequence right-infinite sample sequence sample space satisfying stationary process statistically predictable stochastic semigroup stochastic sequence subprocess subset suppose theorem topologically ergodic transformations transition probabilities unique upper density v-inductive V₁ vanishes vectors w₁ w₂ x₁ Xn+1 Zn+1