Atjaunināt sīkdatņu piekrišanu

Nonlinear Filtering and Smoothing: An Introduction to Martingales, Stochastic Integrals and Estimation [Mīkstie vāki]

4.00/5 (4 ratings by Goodreads)
  • Formāts: Paperback / softback, 336 pages, height x width x depth: 217x139x18 mm, weight: 358 g, illustrations
  • Izdošanas datums: 26-Jul-2005
  • Izdevniecība: Dover Publications Inc.
  • ISBN-10: 0486441644
  • ISBN-13: 9780486441641
Citas grāmatas par šo tēmu:
  • Mīkstie vāki
  • Cena: 34,33 €*
  • * Šī grāmata vairs netiek publicēta. Jums tiks paziņota lietotas grāmatas cena
  • Šī grāmata vairs netiek publicēta. Jums tiks paziņota lietotas grāmatas cena.
  • Daudzums:
  • Ielikt grozā
  • Pievienot vēlmju sarakstam
Nonlinear Filtering and Smoothing: An Introduction to Martingales, Stochastic Integrals and EstimationPalielināt
  • Formāts: Paperback / softback, 336 pages, height x width x depth: 217x139x18 mm, weight: 358 g, illustrations
  • Izdošanas datums: 26-Jul-2005
  • Izdevniecība: Dover Publications Inc.
  • ISBN-10: 0486441644
  • ISBN-13: 9780486441641
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780486441641.html
Keywords:
Appropriate for upper-level undergraduates and graduate students, this volume addresses the fundamental concepts of martingales, stochastic integrals, and estimation. Written by an engineer for engineers, it emphasizes applications.


Appropriate for upper-level undergraduates and graduate students, this volume addresses the fundamental concepts of martingales, stochastic integrals, and estimation. Written by an engineer for engineers, it emphasizes applications. Many theorems feature heuristic proofs; others include rigorous proofs to reinforce physical understanding. Numerous end-of-chapter problems enhance the book's practical value.
1 Basic Concepts of Probability Theory
1(38)
1.1 Introduction,
1(1)
1.2 Algebra of Sets,
1(5)
1.3 Fields, σ-Fields, and Events,
6(4)
1.4 Probability Space,
10(5)
1.5 Random Variables,
15(5)
1.6 Expectation of Random Variables,
20(4)
1.7 Conditioning,
24(5)
1.8 Convergence of Random Variables,
29(3)
1.9 Main Inequalities of Expectations,
32(7)
2 Stochastic Processes
39(36)
2.1 Definition of Stochastic Processes,
39(1)
2.2 Separability and Measurability,
40(8)
2.3 Continuity Concepts,
48(5)
2.4 Classes of Stochastic Processes,
53(11)
2.5 Brownian Motion,
64(11)
3 Martingale Processes
75(34)
3.1 Uniform Integrability,
75(2)
3.2 Stopping Times or Markov Times,
77(6)
3.3 Discrete Martingales and Submartingales,
83(11)
3.4 Continuous Parameter Martingales and Submartingales,
94(5)
3.5 Doob-Meyer Decomposition,
99(10)
4 Classes of Martingales and Related Processes
109(18)
4.1 Square Integrable Martingales,
109(1)
4.2 Martingales with Jumps,
110(2)
4.3 Increasing Processes of Square Integrable Martingales,
112(5)
4.4 Local Martingales,
117(10)
5 White Noise and White Noise Integrals
127(24)
5.1 Introduction,
127(2)
5.2 White Noise,
129(8)
5.3 Spectral Representation,
137(9)
5.4 White Noise Differential Equation,
146(5)
6 Stochastic Integrals and Stochastic Differential Equations
151(42)
6.1 Stochastic Integrals,
151(9)
6.2 Ito Process (Generalized Stochastic Integral),
160(2)
6.3 Ito Formula,
162(3)
6.4 Vector Formulation of Ito's Rule,
165(5)
6.5 Stochastic Integrals on Square Integrable Martingales,
170(7)
6.6 Representation of Square Integrable Martingales,
177(5)
6.7 Extension of Ito's Rule,
182(11)
7 Stochastic Differential Equations
193(30)
7.1 Stochastic Differential Equation,
193(3)
7.2 Differential Equation Driven by White Noise,
196(14)
7.3 Vector Formulation,
210(2)
7.4 Stratonovich Integral,
212(11)
8 Optimal Nonlinear Filtering
223(22)
8.1 Diffusion Processes,
223(3)
8.2 Innovations Process,
226(1)
8.3 Estimation Problem,
227(1)
8.4 Optimal Nonlinear Filtering,
228(11)
8.5 Vector Formulation,
239(6)
9 Optimal Linear Nonstationary Filtering (Kalman — Bucy Filter)
245(26)
9.1 Recursive Estimation,
245(3)
9.2 Discrete Kalman Filter,
248(9)
9.3 Continuous Kalman Filter,
257(6)
9.4 Kalman Filter as a Special Case of the Nonlinear Filter,
263(8)
10 Application of Nonlinear Filtering to Fault Detection Problems 271(22)
10.1 Introduction,
271(1)
10.2 Fault Detection with Change in Plant Parameter ft,
272(9)
10.3 Fault Detection with Change in Signal Noise Parameter gt,
281(5)
10.4 Adaptive Algorithm,
286(3)
10.5 Modeling Other System Changes,
289(4)
11 Optimal Smoothing 293(14)
11.1 Smoothing Problems,
293(2)
11.2 Martingale Representation for Smoothed Estimates,
295(4)
11.3 Linear Smoothing Problem,
299(8)
References 307(4)
Index 311(4)
Errata 315