Author | Ibragimov, I. A. author |
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Title | Gaussian Random Processes [electronic resource] / by I. A. Ibragimov, Y. A. Rozanov |
Imprint | New York, NY : Springer New York, 1978 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-6275-6 |
Descript | X, 277 p. online resource |
I Preliminaries -- I.1 Gaussian Probability Distribution in a Euclidean Space -- I.2 Gaussian Random Functions with Prescribed Probability Measure -- I.3 Lemmas on the Convergence of Gaussian Variables -- I.4 Gaussian Variables in a Hilbert Space -- I.5 Conditional Probability Distributions and Conditional Expectations -- I.6 Gaussian Stationary Processes and the Spectral Representation -- II The Structures of the Spaces H(T) and LT(F) -- II. 1 Preliminaries -- II.2 The Spaces L+(F) and L-(F) -- II.3 The Construction of Spaces LT(F) When T Is a Finite Interval -- II.4 The Projection of L+(F) on L-(F) -- II.5 The Structure of the ?-algebra of Events U(T) -- III Equivalent Gaussian Distributions and their Densities -- III.1 Preliminaries -- III.2 Some Conditions for Gaussian Measures to be Equivalent -- III.3 General Conditions for Equivalence and Formulas for Density of Equivalent Distributions -- III.4 Further Investigation of Equivalence Conditions -- IV Conditions for Regularity of Stationary Random Processes -- IV.1 Preliminaries -- IV.2 Regularity Conditions and Operators Bt -- IV.3 Conditions for Information Regularity -- IV.4 Conditions for Absolute Regularity and Processes with Discrete Time -- IV.5 Conditions for Absolute Regularity and Processes with Continuous Time -- V Complete Regularity and Processes with Discrete Time -- V.l Definitions and Preliminary Constructions with Examples -- V.2 The First Method of Study: HelsonโSarasonโs Theorem -- V.3 The Second Method of Study: Local Conditions -- V.4 Local Conditions (continued) -- V.5 Corollaries to the Basic Theorems with Examples -- V.6 Intensive Mixing -- VI Complete Regularity and Processes with Continuous Time -- VI.1 Introduction -- VI.2 The Investigation of a Particular Function ?(T;ยต) -- VI.3 The Proof of the Basic Theorem on Necessity -- VI.4 The Behavior of the Spectral Density on the Entire Line -- VI.5 Sufficiency -- VI.6 A Special Class of Stationary Processes -- VII Filtering and Estimation of the Mean -- VII.1 Unbiased Estimates -- VII.2 Estimation of the Mean Value and the Method of Least Squares -- VII.3 Consistent Pseudo-Best Estimates -- VII.4 Estimation of Regression Coefficients -- References