An edition of Stochastic processes
(1995)
Stochastic processes
inference theory
by M. M. Rao
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The book presents, for the first time, a detailed analysis of harmonizable processes and fields (in the weak sense) that contain the corresponding stationary theory as a subclass. It also gives the structural and some key applications in detail. These include Levy's Brownian motion, a probabilistic proof of the longstanding Riemann's hypothesis, random fields indexed by LCA and hypergroups, extensions to bistochastic operators, CramérKarhunen classes, as well as bistochastic operators with some statistical applications. The material is accessible to graduate students in probability and statistics as well as to engineers in theoretical applications. There are numerous extensions and applications pointed out in the book that will inspire readers to delve deeper.
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| Edition | Availability |
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1
Stochastic processes: Harmonizable Theory
July 14, 2020, World Scientific Publishing Company Pvt. Ltd.
Hardcover
in English
- First edition
9811213658 9789811213656
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2
Stochastic processes: inference theory
2000, Kluwer Academic Publishers
in English
0792363248 9780792363248
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WorldCat
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3
Stochastic processes: inference theory
2000, Kluwer Academic Publishers
in English
0792363248 9780792363248
|
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Libraries near you:
WorldCat
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4
Stochastic processes: general theory
1995, Kluwer Academic Publishers
in English
0792337255 9780792337256
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Book Details
Table of Contents
Machine generated contents note: Chapter I: Introduction and Preliminaries 1
1.1 The problem of inference1
1.2 Testing a hypothesis4
1.3 Distinguishability of hypotheses7
1.4 Estimation of parameters10
1.5 Inference as a decision problem12
1.6 Complements and exercises15
Bibliographical notes17
Chapter II: Some Principles of Hypothesis Testing 19
2.1 Testing simple hypotheses19
2.2 Reduction of composite hypotheses38
2.3 Composite hypotheses with iterated weights42
2.4 Bayesian methodology for applications 48
2.5 Further results on composite hypotheses55
2.6 Complements and exercises67
Bibliographical notes70
Chapter III: Parameter Estimation and Asymptotics 73
3.1 Loss functions of different types 73
3.2 Existence and other properties of estimators75
3.3 Some principles of estimation 88
3.4 Asymptotics in estimation methodology107
3.5 Sequential estimation117
3.6 Complements and exercises125
Bibliographical notes130
Chapter IV: Inferences for Classes of Processes 133
4.1 Testing methods for second order processes133
4.2 Sequential testing of processes155
4.3 Weighted unbiased linear least squares prediction179
4.4 Estimation in discrete parameter models196
4.5 Asymptotic properties of estimators200
4.6 Complements and exercises213
Bibliographical notes219
Chapter V: Likelihood Ratios for Processes 223
5.1 Sets of admissible signals or translates223
5.2 General Gaussian processes247
5.3 Independent increment and jump Markov processes. 277
5.4 Infinitely divisible processes298
5.5 Diffusion type processes 314
5.6 Complements and exercises327
Bibliographical notes335
Chapter VI: Sampling Methods for Processes 339
6.1 Kotel'nikov-Shannon methodology339
6.2 Band limited sampling348
6.3 Analyticity of second order processes353
6.4 Periodic sampling of processes and fields358
6.5 Remarks on optional sampling374
6.6 Complements and exercises375
Bibliographical notes380
Chapter VII: More on Stochastic Inference 383
7.1 Absolute continuity of families of probability measures 383
7.2 Likelihood ratios for families of non Gaussian measures 405
7.3 Extension to two parameter families of measures413
7.4 Likelihood ratios in statistical communication theory 429
7.5 The general Gaussian dichotomy and Girsanov's theorem 435
7.6 Complements and exercises452
Bibliographical notes462
Chapter VIII: Prediction and Filtering of Processes 465
8.1 Predictors and projections465
8.2 Least squares prediction: the Cram6r-Hida approach 480
8.3 Linear filtering: Bochner's formulatioii488
8.4 Kalman-Bucy filters: the linear case/509
8.5 Kalman-Bucy filters: the nonlinear case535
8.6 Complements and exercises549
Bibliographical notes553
Chapter IX: Nonparametric Estimation for Processes 557
9.1 Spectra for classes of second order processes557
9.2 Asymptotically unbiased estimation of bispectra560
9.3 Resampling procedure and consistent estimation563
9.4 Associated spectral estimation for a class of processes 572
9.5 Limit distributions of (bi)spectral function estimators .583
9.6 Complements and exercises593
Bibliographical notes597
Bibliography 601
Notation index 627
Author index 633
Subject index 639.
Edition Notes
Includes bibliographical references (p. 601-625) and indexes.
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| August 17, 2023 | Edited by ImportBot | import existing book |
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