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Stochastic Modelling and Applied Probability #5: Statistics of Random Processes: I. General Theory

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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:

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

Essentials of probability theory and mathematical statistics.- Martingales and related processes.- Martingales and supermartingales: continuous time.- The Wiener process, the stochastic integral over the Wiener process, and stochastic differential equations.- Square integrable martingales, and structure of the functionals on a Wiener process.- Nonnegative supermartingales and martingales, and the Girsanovs theorem.- Absolute continuity of measures corresponding to the Ito processes and processes of diffusion type.- General equations of optimal nonlinear filtering, interpolation and extrapolation of partially observable random processes.- Optimal filtering, interpolation and extrapolation of Markov processes with countable number of states.- Optimal linear nonstationary filtering.

Product Details

ISBN:
9783642083662
Author:
Liptser, Robert S.
Publisher:
Springer
Author:
Aries, B.
Author:
Shiryaev, Albert N.
Location:
Berlin, Heidelberg
Subject:
Statistics
Subject:
Conditionally Gaussian
Subject:
Filtering
Subject:
Incomplete Data Control
Subject:
martingale
Subject:
Point Process
Subject:
Probability Theory and Stochastic Processes
Subject:
Statistical Theory and Methods
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>In each chapter a
Subject:
Mathematics | Probability and Statistics
Subject:
Mathematics
Subject:
B
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:
5
Publication Date:
20101208
Binding:
TRADE PAPER
Language:
English
Pages:
442
Dimensions:
235 x 155 mm 666 gr

Related Subjects


Science and Mathematics » Mathematics » Analysis 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 #5: Statistics of Random Processes: I. General Theory New Trade Paper
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Product details 442 pages Springer - English 9783642083662 Reviews:
"Synopsis" by , 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.
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