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Stochastic Modelling and Applied Probability #6: Statistics of Random Processes: II. Applications

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Stochastic Modelling and Applied Probability #6: Statistics of Random Processes: II. Applications Cover

 

Synopses & Reviews

Publisher Comments:

The subject of these two volumes is non-linear filtering (prediction and smoothing) theory and its application to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. The required mathematical background is presented in the first volume: the theory of martingales, stochastic differential equations, the absolute continuity of probability measures for diffusion and Ito processes, elements of stochastic calculus for counting processes. The book is not only addressed to mathematicians but should also serve the interests of other scientists who apply probabilistic and statistical methods in their work. The theory of martingales presented in the book has an independent interest in connection with problems from financial mathematics. In the second edition, the authors have made numerous corrections, updating every chapter, adding two new subsections devoted to the Kalman filter under wrong initial conditions, as well as a new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years.

Synopsis:

"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

Conditionally Gaussian processes.- Optimal nonlinear filtering, interpolation, and extrapolation of components of conditionally Gaussian processes.- Conditionally Gaussian sequences:filtering and related problems.- Application of filtering equations to problems of statistics of random sequences.- Linear Estimation of random processes.- Application of optimal nonlinear filtering equations to some problems in control theory and information theory.- Parameter estimation and testing of statistical hypotheses for diffusion type processes.- Random point processes: Stieltjes stochastic integrals.- The structure of local martingales, absolute continuity of measures for point processes, and filtering.- Asymptotically optimal filtering

Product Details

ISBN:
9783642083655
Author:
Liptser, Robert S.
Publisher:
Springer
Author:
Shiryaev, Albert N.
Author:
Aries, A. B.
Location:
Berlin, Heidelberg
Subject:
Statistics
Subject:
Filtering
Subject:
Incomplete Data Control
Subject:
martingale
Subject:
Point Process
Subject:
Conditionally Gaussian
Subject:
Probability Theory and Stochastic Processes
Subject:
Statistical Theory and Methods In the second edition, two new subsections devoted to the Kalman filter under wrong initial conditions, and a new chapter on asymptotically optimal filtering under diffusion approximation have been added<BR>Moreover in each
Subject:
Mathematics | Probability and Statistics
Subject:
Statistical Theory and Methods
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Distribution (Probability theory)
Subject:
Mathematical statistics
Copyright:
Edition Description:
Softcover reprint of hardcover 2nd ed. 2001
Series:
Stochastic Modelling and Applied Probability
Series Volume:
6
Publication Date:
20101201
Binding:
TRADE PAPER
Language:
English
Pages:
417
Dimensions:
235 x 155 mm 631 gr

Related Subjects


Science and Mathematics » Environmental Studies » Environment
Science and Mathematics » Materials Science » General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Stochastic Modelling and Applied Probability #6: Statistics of Random Processes: II. Applications New Trade Paper
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Product details 417 pages Springer - English 9783642083655 Reviews:
"Synopsis" by , "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
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