Statistics of random processes

Author(s)

• Lipt︠s︡er, R. Sh. (Robert Shevilevich)
• Shiri︠a︡ev, Alʹbert Nikolaevich

Bibliographic Information

Statistics of random processes

Robert S. Liptser, Albert N. Shiryaev ; translated by A.B. Aries ; translation editor, Stephen S. Wilson

（Applications of mathematics, 5-6）

Springer, c2001

2nd, rev. and expanded ed

• 1
• 2

Other Title

Statistika sluchaĭnykh prot︠s︡essov

Note

1. General theory -- 2. Applications

Includes bibliographical references and indexes

Description and Table of Contents

Volume

2 ISBN 9783540639282

Description

"Written by two renowned experts in the field, the books under review contain a thorough and insightful treatment of the fundamental underpinnings of various aspects of stochastic processes as well as a wide range of applications. Providing clear exposition, deep mathematical results, and superb technical representation, they are masterpieces of the subject of stochastic analysis and nonlinear filtering....These books...will become classics." --SIAM REVIEW

Table of Contents

11. Conditionally Gaussian Processes.- 12. Optimal Nonlinear Filtering: Interpolation and Extrapolation of Components of Conditionally Gaussian Processes.- 13. Conditionally Gaussian Sequences: Filtering and Related Problems.- 14. Application of Filtering Equations to Problems of Statistics of Random Sequences.- 15. Linear Estimation of Random Processes.- 16. Application of Optimal Nonlinear Filtering Equations to some Problems in Control Theory and Estimation Theory.- 17. Parameter Estimation and Testing of Statistical Hypotheses for Diffusion-Type Processes.- 18. Random Point Processes: Stieltjes Stochastic Integrals.- 19. The Structure of Local Martingales, Absolute Continuity of Measures for Point Processes, and Filtering.- 20. Asymptotically Optimal Filtering.

Volume

1 ISBN 9783540639299

Description

These volumes cover non-linear filtering (prediction and smoothing) theory and its applications to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. Also presented is the theory of martingales, of interest to those who deal with problems in financial mathematics. These editions include new material, expanded chapters, and comments on recent progress in the field.

Table of Contents

1. Essentials of Probability Theory and Mathematical Statistics.- 2. Martingales and Related Processes: Discrete Time.- 3. Martingales and Related Processes: Continuous Time.- 4. The Wiener Process, the Stochastic Integral over the Wiener Process, and Stochastic Differential Equations.- 5. Square Integrable Martingales and Structure of the Functionals on a Wiener Process.- 6. Nonnegative Supermartingales and Martingales, and the Girsanov Theorem.- 7. Absolute Continuity of Measures corresponding to the Ito Processes and Processes of the Diffusion Type.- 8. General Equations of Optimal Nonlinear Filtering, Interpolation and Extrapolation of Partially Observable Random Processes.- 9. Optimal Filtering, Interpolation and Extrapolation of Markov Processes with a Countable Number of States.- 10. Optimal Linear Nonstationary Filtering.

by "Nielsen BookData"

Details

• NCID: BA49486760
• ISBN:
  • 3540639292
  • 9783540639282
• LCCN: 00041918
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: rus
• Place of Publication: Berlin ; New York
• Pages/Volumes: v.
• Size: 24 cm
• Classification:
  • LCC : QA274
  • DC21 : 519.2/3
  • NDC9 : 417.1
• Subject Headings:
  • LCSH : Stochastic processes
  • LCSH : Mathematical statistics
• Parent Bibliography ID:
  • BA00256802