Stochastic filtering theory / Gopinath Kallianpur.

Por: Kallianpur, GSeries Applications of mathematics ; 13Editor: New York : Springer-Verlag, c1980Descripción: xvi, 316 p. : ill. ; 25 cmISBN: 038790445XTema(s): Stochastic processes | Filters (Mathematics) | Prediction theoryOtra clasificación: *CODIGO*
Contenidos:
Standard Notation xv --
Chapter 1 Stochastic Processes: Basic Concepts and Definitions [1] --
1.1 Notation and Basic Definitions [1] --
1.2 Probability Measures Associated with Stochastic Processes [6] --
Chapter 2 Martingales and the Wiener Process [12] --
2.1 The Wiener Process [12] --
2.2 Martingales and Super mart ingales [18] --
2.3 Properties of Wiener Processes Wiener Martingales [20] --
2.4 Decomposition of Superman ingales [24] --
2.5 The Quadratic Variation of a Square Integrable Martingale [33] --
2.6 Local Martingales [37] --
2.7 Some Useful Theorems [45] --
Chapter 3 Stochastic Integrals [48] --
3.1 Predictable Processes [48] --
3.2 Stochastic Integrals for L2-Martingales [52] --
3.3 The Ito Integral [59] --
3.4 The Stochastic Integral with Respect to Continuous Local Martingales [70] --
Chapter 4 The Ito Formula [77] --
4.1 Vector-Valued Processes [77] --
4.2 The Ito Formula [78] --
4.3 Ito Formula (General Version) [84] --
4.4 Applications of the ho Formula [88] --
4.5 A Vector- Valued Version of Ito’s Formula [92] --
Chapter 5 Stochastic Differential Equations [94] --
5.1 Existence and Uniqueness of Solutions [94] --
5.2 Strong and Weak Solutions [105] --
5.3Linear Stochastic Differential Equations [108] --
5.4 Markov Processes [111] --
5.5 Extended Generator of £(r) [120] --
5.6 Diffusion Processes [124] --
5.7 Existence of Moments [127] --
Chapter 6 Functionals of a Wiener Process [134] --
6.1 Introduction [134] --
6.2 The Multiple Wiener Integral [134]
6.3 Hilbert Spaces Associated with a Gaussian Process [139] --
6.4 Tensor Products and Symmetric Tensor Products of Hilbert Spaces [139] --
6.5 CONS in ... [144]
6.6 Homogeneous Chaos [145] --
6.7 Stochastic (Ito) Integral Representation [155] --
6.8 A Generalization of Theorem 6.7.3 [159] --
Chapter 7 Absolute Continuity of Measures and Radon-Nikodym Derivatives [162] --
7.1 Exponential Supermaningales. Martingales, and Girsanov’s Theorem [162] --
7.2 Sufficient Conditions for the Validity of Girsanov’s Theorem [172] --
7. 3 Stochastic Equations and Absolute Continuity of Induced Measures [174] --
7.4 Weak Solutions [179] --
7.5 Stochastic Equations Involving --
Vector-Valued Processes [181] --
7.6 Explosion Times and an Extension of Girsanov’s Formula [182] --
7.7 Nonefistence of a Strong Solution [189] --
Chapter 8 The General Filtering Problem and the Stochastic Equation of the Optimal Filter (Part I)192 --
8.1 The Filtering Problem and the Innovation Process [192] --
8.2 Observation Process Model with Absolutely Continuous (S,) [204] --
8.3 Stochastic Integral Representation of a Separable Martingale on (Q,.^.P) [208] --
8.4 A Stochastic Equation for the General Nonlinear Filtering Problem [210] --
8.5 Applications [220] --
8.6 The Case of Markov Processes [221] --
Chapter 9 Gaussian Solutions of Stochastic Equations [225] --
9.1 The Gohberg-Krcin Factorization Theorem [225] --
9.2 Nonanticipativc Representations of Equivalent Gaussian Processes [230] --
9.3 Nonanticipative Representation of a Gaussian --
Process Equivalent to a Wiener Process [232] --
9.4 Gaussian Solutions of Stochastic Equations [233] --
9.5 Vector-Valued Processes [244] --
Chapter 10 Linear Filtering Theory [247] --
10.1 Introduction [247] --
10.2 The Stochastic Model for the Kalman Theory [252] --
10.3 Derivation of the Kalman Filter from the Nonlinear Theory [256] --
10.4 The Filtering Problem for Gaussian Processes [260] --
10.5 The Kalman Filter (Independent Derivation) [266] --
Chapter 11 The Stochastic Equation of the Optimal Filter (Part II) [273] --
11.1 Introduction [273] --
11.2 A Stochastic Differential Equation for the Conditional Density [274] --
11.3 A Bayes Formula for Stochastic Processes [278] --
11.4 Equality of the Sigma Fields .Ff and .F* [283] --
11.5 Solution of the Filter Equation [287] --
Notes [295] --
References [305] --
Index of Commonly Used Symbols [311] --
Index [313] --
List(s) this item appears in: Últimas adquisiciones
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Libros Libros Instituto de Matemática, CONICET-UNS
Libros ordenados por tema 60 K145s (Browse shelf) Available A-9353

"Based on a seminar given at the University of California at Los Angeles in the spring of 1975."

Includes indexes.

Bibliografía: p. 305-309.

Standard Notation xv --
Chapter 1 Stochastic Processes: Basic Concepts and Definitions [1] --
1.1 Notation and Basic Definitions [1] --
1.2 Probability Measures Associated with Stochastic Processes [6] --
Chapter 2 Martingales and the Wiener Process [12] --
2.1 The Wiener Process [12] --
2.2 Martingales and Super mart ingales [18] --
2.3 Properties of Wiener Processes Wiener Martingales [20] --
2.4 Decomposition of Superman ingales [24] --
2.5 The Quadratic Variation of a Square Integrable Martingale [33] --
2.6 Local Martingales [37] --
2.7 Some Useful Theorems [45] --
Chapter 3 Stochastic Integrals [48] --
3.1 Predictable Processes [48] --
3.2 Stochastic Integrals for L2-Martingales [52] --
3.3 The Ito Integral [59] --
3.4 The Stochastic Integral with Respect to Continuous Local Martingales [70] --
Chapter 4 The Ito Formula [77] --
4.1 Vector-Valued Processes [77] --
4.2 The Ito Formula [78] --
4.3 Ito Formula (General Version) [84] --
4.4 Applications of the ho Formula [88] --
4.5 A Vector- Valued Version of Ito’s Formula [92] --
Chapter 5 Stochastic Differential Equations [94] --
5.1 Existence and Uniqueness of Solutions [94] --
5.2 Strong and Weak Solutions [105] --
5.3Linear Stochastic Differential Equations [108] --
5.4 Markov Processes [111] --
5.5 Extended Generator of £(r) [120] --
5.6 Diffusion Processes [124] --
5.7 Existence of Moments [127] --
Chapter 6 Functionals of a Wiener Process [134] --
6.1 Introduction [134] --
6.2 The Multiple Wiener Integral [134]
6.3 Hilbert Spaces Associated with a Gaussian Process [139] --
6.4 Tensor Products and Symmetric Tensor Products of Hilbert Spaces [139] --
6.5 CONS in ... [144]
6.6 Homogeneous Chaos [145] --
6.7 Stochastic (Ito) Integral Representation [155] --
6.8 A Generalization of Theorem 6.7.3 [159] --
Chapter 7 Absolute Continuity of Measures and Radon-Nikodym Derivatives [162] --
7.1 Exponential Supermaningales. Martingales, and Girsanov’s Theorem [162] --
7.2 Sufficient Conditions for the Validity of Girsanov’s Theorem [172] --
7. 3 Stochastic Equations and Absolute Continuity of Induced Measures [174] --
7.4 Weak Solutions [179] --
7.5 Stochastic Equations Involving --
Vector-Valued Processes [181] --
7.6 Explosion Times and an Extension of Girsanov’s Formula [182] --
7.7 Nonefistence of a Strong Solution [189] --
Chapter 8 The General Filtering Problem and the Stochastic Equation of the Optimal Filter (Part I)192 --
8.1 The Filtering Problem and the Innovation Process [192] --
8.2 Observation Process Model with Absolutely Continuous (S,) [204] --
8.3 Stochastic Integral Representation of a Separable Martingale on (Q,.^.P) [208] --
8.4 A Stochastic Equation for the General Nonlinear Filtering Problem [210] --
8.5 Applications [220] --
8.6 The Case of Markov Processes [221] --
Chapter 9 Gaussian Solutions of Stochastic Equations [225] --
9.1 The Gohberg-Krcin Factorization Theorem [225] --
9.2 Nonanticipativc Representations of Equivalent Gaussian Processes [230] --
9.3 Nonanticipative Representation of a Gaussian --
Process Equivalent to a Wiener Process [232] --
9.4 Gaussian Solutions of Stochastic Equations [233] --
9.5 Vector-Valued Processes [244] --
Chapter 10 Linear Filtering Theory [247] --
10.1 Introduction [247] --
10.2 The Stochastic Model for the Kalman Theory [252] --
10.3 Derivation of the Kalman Filter from the Nonlinear Theory [256] --
10.4 The Filtering Problem for Gaussian Processes [260] --
10.5 The Kalman Filter (Independent Derivation) [266] --
Chapter 11 The Stochastic Equation of the Optimal Filter (Part II) [273] --
11.1 Introduction [273] --
11.2 A Stochastic Differential Equation for the Conditional Density [274] --
11.3 A Bayes Formula for Stochastic Processes [278] --
11.4 Equality of the Sigma Fields .Ff and .F* [283] --
11.5 Solution of the Filter Equation [287] --
Notes [295] --
References [305] --
Index of Commonly Used Symbols [311] --
Index [313] --

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