Linear processes in function spaces. Theory and applications.

*(English)*Zbl 0962.60004
Lecture Notes in Statistics. 149. New York, NY: Springer. xiii, 283 p. (2000).

This book is devoted to study linear processes in Hilbert and Banach spaces and applications of them to statistics of continuous time processes. The book is self-contained for those with some background in probability theory and statistics. All necessary informations on stochastic processes in Hilbert and Banach spaces are given in Chapters 1 and 2. The main tool, very often used, is representation of continuous time stochastic processes as random variables in function spaces. Chapters 3 to 5 are devoted to autoregressive processes in Hilbert space (basic properties, stationarity, limit theorems, estimations of different characteristics). Autoregressive processes with values in separable Banach space are described in Chapter 6. General linear processes are investigated in Chapter 7. Chapter 8 is devoted to estimation of autocorrelation operator (there are considered finite-dimensional as well as infinite-dimensional case) and prediction. In the final Chapter 9 numerous examples of applications with implementations and numerical results in various fields are given.

Reviewer: J.Jakubowski (Warszawa)

##### MSC:

60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62M20 | Inference from stochastic processes and prediction |

60G25 | Prediction theory (aspects of stochastic processes) |