Topics in stochastic processes / / Robert B. Ash, Melvin F. Gardner

• Record Nr.: UNINA9910812507203321
• Autore: Ash Robert B.
• Pubbl/distr/stampa: New York, New York ; ; London, England : , : Academic Press, , 1975; ©1975
• ISBN: 1-4831-9143-5
• Descrizione fisica: 1 online resource (332 p.)
• Collana: Probability and Mathematical Statistics ; ; Volume 27
• Disciplina: 519.2
• Soggetti: Stochastic processes
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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
• Sommario/riassunto: Topics in Stochastic Processes