03627nam 2200565 450 991081250720332120230120014641.01-4831-9143-5(CKB)3710000000200380(EBL)1901370(SSID)ssj0001267423(PQKBManifestationID)12470246(PQKBTitleCode)TC0001267423(PQKBWorkID)11255630(PQKB)11055264(MiAaPQ)EBC1901370(EXLCZ)99371000000020038020150119h19751975 uy 0engur|n|---|||||txtccrTopics in stochastic processes /Robert B. Ash, Melvin F. GardnerNew York, New York ;London, England :Academic Press,1975.©19751 online resource (332 p.)Probability and Mathematical Statistics ;Volume 27Description based upon print version of record.1-322-55686-5 0-12-065270-6 Includes bibliographical references and index.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 Processes2.7 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 Motion4.4 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 TheoremAppendix 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; IndexTopics in Stochastic ProcessesProbability and mathematical statistics ;Volume 27.Stochastic processesStochastic processes.519.2Ash Robert B.140703Gardner Melvin F.MiAaPQMiAaPQMiAaPQBOOK9910812507203321Topics in stochastic processes918808UNINA