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Topics in stochastic processes

Author: Robert B Ash; Melvin Frank Gardner; Z W Birnbaum; E Lukacs
Publisher: Burlington : Academic Press/Elsevier Science, [2014], ©1975.
Series: Probability and mathematical statistics, v. 27.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Topics in Stochastic Processes.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ash, Robert B.
Topics in Stochastic Processes : Probability and Mathematical Statistics: A Series of Monographs and Textbooks.
Burlington : Elsevier Science, ©2014
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Robert B Ash; Melvin Frank Gardner; Z W Birnbaum; E Lukacs
ISBN: 9781483191430 1483191435
OCLC Number: 898771933
Description: 1 online resource (332 pages).
Contents: Front Cover; Topics in Stochastic Processes; Copyright Page; Table of Contents; PREFACE; Chapter 1. L2 Stochastic Processes; 1.1 Introduction; 1.2 Covariance Functions; 1.3 Second Order Calculus; 1.4 Karhunen-Loève Expansion; 1.5 Estimation Problems; 1.6 Notes; Chapter 2. Spectral Theory and Prediction; 2.1 Introduction; L2 Stochastic Integrals; 2.2 Decomposition of Stationary Processes; 2.3 Examples of Discrete Parameter Processes; 2.4 Discrete Parameter Prediction: Special Cases; 2.5 Discrete Parameter Prediction: General Solution; 2.6 Examples of Continuous Parameter Processes. 2.7 Continuous Parameter Prediction in Special Cases Yaglom's Method; 2.8 Some Stochastic Differential Equations; 2.9 Continuous Parameter Prediction: Remarks on the General Solution; 2.10 Notes; Chapter 3. Ergodic Theory; 3.1 Introduction; 3.2 Ergodicity and Mixing; 3.3 The Pointwise Ergodic Theorem; 3.4 Applications to Real Analysis; 3.5 Applications to Markov Chains; 3.6 The Shannon-McMillan Theorem; 3.7 Notes; Chapter 4. Sample Function Analysis of Continuous Parameter Stochastic Processes; 4.1 Separability; 4.2 Measurability; 4.3 One-Dimensional Brownian Motion. 4.4 Law of the Iterated Logarithm4.5 Markov Processes; 4.6 Processes with Independent Increments; 4.7 Continuous Parameter Martingales; 4.8 The Strong Markov Property; 4.9 Notes; Chapter 5. The Itô Integral and Stochastic Differential Equations; 5.1 Definition of the Itô Integral; 5.2 Existence and Uniqueness Theorems for Stochastic Differential Equations; 5.3 Stochastic Differentials: A Chain Rule; 5.4 Notes; Appendix 1: Some Results from Complex Analysis; A1.1 Definitions and Comments; A1.2 Lemma; A1.3 Fatou's Radial Limit Theorem; A1.4 The Space H; A1.5 Theorem; A1.6 Theorem; A1.7 Theorem. Appendix 2: Fourier Transforms on the Real LineA2.1 Some Basic Properties; A2.2 Lemma; A2.3 Lemma; A2.4 Lemma; A2.5 Inversion Theorem; A2.6 Fourier-Plancherel Theorem; References; Solutions to Problems; Index.
Series Title: Probability and mathematical statistics, v. 27.
Responsibility: Robert B. Ash, Melvin F. Gardner.

Abstract:

Topics in Stochastic Processes.

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