Stationary stochastic processes. (Statsionarnye sluchajnye protsessy). 2nd ed., compl. (Statsionarnye sluchajnye protsessy.) (Russian) Zbl 0721.60040

Rozanov, Yu. A.

Teoriya Veroyatnostej i Matematicheskaya Statistika, 42. Moskva: Nauka. 272 p. R. 2.80 (1990).

[For the first edition (1963) see Zbl 0121.126].
This book is considered to be one of the fundamental and the most complete guide to the theory of stationary stochastic processes. Explanation of the theme is very compact thanks to the fact that from the beginning it is performed for multivariate processes. In addition to the spectral theory of stochastic processes, the author explains a number of problems concerning the theory of stationary processes in a closer sense (e.g. ergodic properties, Gaussian processes, limit theorems). Readers are expected to be acquainted with the foundations of the theory of stochastic processes.
This book is intended first for undergraduate and postgraduate students of mathematical and physical specializations at universities. It may be also useful for scientific workers specialized in the study of stochastic processes.
Chapter headings: (1) Harmonic analysis of stationary stochastic processes; (2) Linear predicting stationary processes with a discrete time; (3) Linear predicting stationary processes with a continuous time; (4) Stationary stochastic processes in a closer sense.

Reviewer: I.Křivý (Ostrava)

MSC:

60G10	Stationary stochastic processes
60-02	Research exposition (monographs, survey articles) pertaining to probability theory

Keywords:

stationary stochastic processes; spectral theory; ergodic properties; Gaussian processes; Linear predicting