LEADER 03627nam 2200565 450 001 9910812507203321 005 20230120014641.0 010 $a1-4831-9143-5 035 $a(CKB)3710000000200380 035 $a(EBL)1901370 035 $a(SSID)ssj0001267423 035 $a(PQKBManifestationID)12470246 035 $a(PQKBTitleCode)TC0001267423 035 $a(PQKBWorkID)11255630 035 $a(PQKB)11055264 035 $a(MiAaPQ)EBC1901370 035 $a(EXLCZ)993710000000200380 100 $a20150119h19751975 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTopics in stochastic processes /$fRobert B. Ash, Melvin F. Gardner 210 1$aNew York, New York ;$aLondon, England :$cAcademic Press,$d1975. 210 4$dİ1975 215 $a1 online resource (332 p.) 225 1 $aProbability and Mathematical Statistics ;$vVolume 27 300 $aDescription based upon print version of record. 311 $a1-322-55686-5 311 $a0-12-065270-6 320 $aIncludes bibliographical references and index. 327 $aFront 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-Loe?ve 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 327 $a2.7 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 327 $a4.4 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 Ito? Integral and Stochastic Differential Equations; 5.1 Definition of the Ito? 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 327 $aAppendix 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 330 $aTopics in Stochastic Processes 410 0$aProbability and mathematical statistics ;$vVolume 27. 606 $aStochastic processes 615 0$aStochastic processes. 676 $a519.2 700 $aAsh$b Robert B.$0140703 702 $aGardner$b Melvin F. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910812507203321 996 $aTopics in stochastic processes$9918808 997 $aUNINA