| Preface | |
| Notation | |
| Synopsis | p. 1 |
| Stochastic processes and random variables in function spaces | p. 15 |
| Stochastic processes | p. 15 |
| Random functions | p. 21 |
| Expectation and conditional expectation in Banach spaces | p. 27 |
| Covariance operators and characteristic functionals in Banach spaces | p. 30 |
| Random variables and operators in Hilbert spaces | p. 33 |
| Linear prediction in Hilbert spaces | p. 38 |
| Sequences of random variables in Banach spaces | p. 43 |
| Stochastic processes as sequences of B-valued random variables | p. 43 |
| Convergence of B-random variables | p. 44 |
| Limit theorems for i.i.d. sequences of B-random variables | p. 47 |
| Sequences of dependent random variables in Banach spaces | p. 54 |
| Derivation of exponential bounds | p. 66 |
| Autoregressive Hilbertian processes of order one | p. 71 |
| Stationarity and innovation in Hilbert spaces | p. 71 |
| The ARH(1) model | p. 73 |
| Basic properties of ARH(1) processes | p. 79 |
| ARH(1) processes with symmetric compact autocorrelation operator | p. 82 |
| Limit theorems for ARH(1) processes | p. 86 |
| Estimation of autocovariance operators for ARH(1) processes | p. 95 |
| Estimation of the covariance operator | p. 95 |
| Estimation of the eigenelements of C | p. 102 |
| Estimation of the cross-covariance operators | p. 112 |
| Limits in distribution | p. 118 |
| Autoregressive Hilbertian processes of order p | p. 127 |
| The ARH(p) model | p. 127 |
| Second order moments of ARH(p) | p. 133 |
| Limit theorems for ARH(p) processes | p. 136 |
| Estimation of autocovariance of an ARH(p) | p. 140 |
| Estimation of the autoregression order | p. 143 |
| Autoregressive processes in Banach spaces | p. 147 |
| Strong autoregressive processes in Banach spaces | p. 147 |
| Autoregressive representation of some real continuous-time processes | p. 150 |
| Limit theorems | p. 153 |
| Weak Banach autoregressive processes | p. 161 |
| Estimation of autocovariance | p. 164 |
| The case of C[0,1] | p. 168 |
| Some applications to real continuous-time processes | p. 175 |
| General linear processes in function spaces | p. 181 |
| Existence and first properties of linear processes | p. 182 |
| Invertibility of linear processes | p. 184 |
| Markovian representations of LPH: applications | p. 188 |
| Limit theorems for LPB and LPH | p. 191 |
| Derivation of invertibility | p. 195 |
| Estimation of autocorrelation operator and prediction | p. 203 |
| Estimation of p if H is finite dimensional | p. 204 |
| Estimation of p in a special case | p. 211 |
| The general situation | p. 218 |
| Estimation of autocorrelation operator in C[0,1] | p. 222 |
| Statistical prediction | p. 226 |
| Derivation of strong consistency | p. 229 |
| Implementation of functional autoregressive predictors and numerical applications | p. 237 |
| Functional data | p. 237 |
| Choosing and estimating a model | p. 240 |
| Statistical methods of prediction | p. 243 |
| Some numerical applications | p. 247 |
| Measure and probability | p. 263 |
| Random variables | p. 264 |
| Function spaces | p. 265 |
| Basic function spaces | p. 266 |
| Conditional expectation | p. 267 |
| Stochastic integral | p. 267 |
| References | p. 269 |
| Index | p. 277 |
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