STATIONARY STOCHASTIC MODELS: AN INTRODUCTION

This volume provides a unified mathematical introduction to stationary time series models and to continuous time stationary stochastic processes. The analysis of these stationary models is carried out in time domain and in frequency domain. It begins with a practical discussion on stationarity, by which practical methods for obtaining stationary data are described. The presented topics are illustrated by numerous examples. Readers will find the following covered in a comprehensive manner:

At the end, some selected topics such as stationary random fields, simulation of Gaussian stationary processes, time series for planar directions, large deviations approximations and results of information theory are presented. A detailed appendix containing complementary materials will assist the reader with many technical aspects of the book.

Contents:
Introduction:Stationary Stochastic Models and OutlineFourier AnalysisStationary Time Series:IntroductionARMA Time SeriesAutocovariance and Related FunctionsAnalysis in Frequency DomainFurther Classical Topics on Time SeriesStationary Processes with Continuous Time:IntroductionImportant Stochastic ProcessesMean Square Properties of Stationary ProcessesStochastic IntegralsSpectral Distribution and Autocovariance FunctionSpectral Decomposition of Stationary Processes and the Spectral TheoremSpectral Analysis of Gaussian ProcessesSpectral Analysis of Counting ProcessesTime Invariant Linear FiltersSelected Topics on Stationary Models:Stationary Random FieldsCircular Time SeriesLong Range DependenceNonintegrable Spectral Density and Intrinsic StationarityUnstable SystemHilbert Transform and EnvelopeSimulation of Stationary Gaussian ProcessesLarge Deviations Theory for Time SeriesInformation Theoretic Results for Time SeriesAppendices:Mathematical ComplementsAbbreviations, Mathematical Notation and Data
Readership: Upper-level undergraduate and graduate students, for lectures on time series or on stochastic processes with continuous time. Researchers in academia and applied scientists in the industry, in the field of time series or stationary processes. These lectures can be given to students of mathematics or statistics as well as to students from other technical fields, at Bachelor's upper-level and at Master's level.

Key Features:
The topics are presented progressively, by going from discrete to continuous time, by studying connected questions and by completing abstract theory with compelling examplesSuited for upper-level undergraduate and graduate students, researchers in academia and scientists in industryCovers both fundamentals and practical aspects of stationary modelsThis book provides a unified presentation of stationary time series and continuous time stationary processesThe appendix provides complementary material that assists the reader with technical aspects of the book