Measure Theory And Filtering

Author : Lakhdar Aggoun,Robert J. Elliott
Publisher : Cambridge University Press
Page : 274 pages
File Size : 53,5 Mb
Release : 2004-09-13
Category : Mathematics
ISBN : 1139456245

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Measure Theory and Filtering by Lakhdar Aggoun,Robert J. Elliott Pdf

The estimation of noisily observed states from a sequence of data has traditionally incorporated ideas from Hilbert spaces and calculus-based probability theory. As conditional expectation is the key concept, the correct setting for filtering theory is that of a probability space. Graduate engineers, mathematicians and those working in quantitative finance wishing to use filtering techniques will find in the first half of this book an accessible introduction to measure theory, stochastic calculus, and stochastic processes, with particular emphasis on martingales and Brownian motion. Exercises are included. The book then provides an excellent users' guide to filtering: basic theory is followed by a thorough treatment of Kalman filtering, including recent results which extend the Kalman filter to provide parameter estimates. These ideas are then applied to problems arising in finance, genetics and population modelling in three separate chapters, making this a comprehensive resource for both practitioners and researchers.

Author : Alan Bain,Dan Crisan
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 41,8 Mb
Release : 2008-10-08
Category : Mathematics
ISBN : 9780387768960

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Fundamentals of Stochastic Filtering by Alan Bain,Dan Crisan Pdf

This book provides a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient background to enable study of the recent literature. While no prior knowledge of stochastic filtering is required, readers are assumed to be familiar with measure theory, probability theory and the basics of stochastic processes. Most of the technical results that are required are stated and proved in the appendices. Exercises and solutions are included.

Author : J.M. Belley,J. Dubois,P. Morales
Publisher : Springer
Page : 335 pages
File Size : 48,7 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540386902

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Measure Theory and its Applications by J.M. Belley,J. Dubois,P. Morales Pdf

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Author : J. Hamhalter
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 51,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401701198

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Quantum Measure Theory by J. Hamhalter Pdf

This book is the first systematic treatment of measures on projection lattices of von Neumann algebras. It presents significant recent results in this field. One part is inspired by the Generalized Gleason Theorem on extending measures on the projection lattices of von Neumann algebras to linear functionals. Applications of this principle to various problems in quantum physics are considered (hidden variable problem, Wigner type theorems, decoherence functional, etc.). Another part of the monograph deals with a fascinating interplay of algebraic properties of the projection lattice with the continuity of measures (the analysis of Jauch-Piron states, independence conditions in quantum field theory, etc.). These results have no direct analogy in the standard measure and probability theory. On the theoretical physics side, they are instrumental in recovering technical assumptions of the axiomatics of quantum theories only by considering algebraic properties of finitely additive measures (states) on quantum propositions.

Author : Andrew H. Jazwinski
Publisher : Academic Press
Page : 376 pages
File Size : 43,5 Mb
Release : 1970-01-31
Category : Mathematics
ISBN : 9780080960906

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Stochastic Processes and Filtering Theory by Andrew H. Jazwinski Pdf

This book presents a unified treatment of linear and nonlinear filtering theory for engineers, with sufficient emphasis on applications to enable the reader to use the theory. The need for this book is twofold. First, although linear estimation theory is relatively well known, it is largely scattered in the journal literature and has not been collected in a single source. Second, available literature on the continuous nonlinear theory is quite esoteric and controversial, and thus inaccessible to engineers uninitiated in measure theory and stochastic differential equations. Furthermore, it is not clear from the available literature whether the nonlinear theory can be applied to practical engineering problems. In attempting to fill the stated needs, the author has retained as much mathematical rigor as he felt was consistent with the prime objective—to explain the theory to engineers. Thus, the author has avoided measure theory in this book by using mean square convergence, on the premise that everyone knows how to average. As a result, the author only requires of the reader background in advanced calculus, theory of ordinary differential equations, and matrix analysis.

Author : D. H. Fremlin
Publisher : Torres Fremlin
Page : 292 pages
File Size : 41,8 Mb
Release : 2000
Category : Fourier analysis
ISBN : 9780953812950

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Measure Theory by D. H. Fremlin Pdf

Author : Andrew H. Jazwinski
Publisher : Courier Corporation
Page : 404 pages
File Size : 49,6 Mb
Release : 2013-04-15
Category : Science
ISBN : 9780486318196

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Stochastic Processes and Filtering Theory by Andrew H. Jazwinski Pdf

This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well. Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probability theory and stochastic processes, the author introduces and defines the problems of filtering, prediction, and smoothing. He presents the mathematical solutions to nonlinear filtering problems, and he specializes the nonlinear theory to linear problems. The final chapters deal with applications, addressing the development of approximate nonlinear filters, and presenting a critical analysis of their performance.

Author : G. Kallianpur,D. Kölzow
Publisher : Springer
Page : 259 pages
File Size : 46,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540355564

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Measure Theory. Applications to Stochastic Analysis by G. Kallianpur,D. Kölzow Pdf

Author : Ali Saberi,Anton A. Stoorvogel,Peddapullaiah Sannuti
Publisher : Springer Science & Business Media
Page : 723 pages
File Size : 52,6 Mb
Release : 2007-10-20
Category : Technology & Engineering
ISBN : 9780817645649

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Filtering Theory by Ali Saberi,Anton A. Stoorvogel,Peddapullaiah Sannuti Pdf

Authors are experts in the field and have published books as well as articles in first-rate journals Comprehensive resource that contains many MATLAB-based examples

Author : Adrian Pizzinga
Publisher : Springer Science & Business Media
Page : 66 pages
File Size : 48,8 Mb
Release : 2012-07-25
Category : Mathematics
ISBN : 9781461447382

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Restricted Kalman Filtering by Adrian Pizzinga Pdf

​​​​​​​​ ​In statistics, the Kalman filter is a mathematical method whose purpose is to use a series of measurements observed over time, containing random variations and other inaccuracies, and produce estimates that tend to be closer to the true unknown values than those that would be based on a single measurement alone. This Brief offers developments on Kalman filtering subject to general linear constraints. There are essentially three types of contributions: new proofs for results already established; new results within the subject; and applications in investment analysis and macroeconomics, where the proposed methods are illustrated and evaluated. The Brief has a short chapter on linear state space models and the Kalman filter, aiming to make the book self-contained and to give a quick reference to the reader (notation and terminology). The prerequisites would be a contact with time series analysis in the level of Hamilton (1994) or Brockwell & Davis (2002) and also with linear state models and the Kalman filter – each of these books has a chapter entirely dedicated to the subject. The book is intended for graduate students, researchers and practitioners in statistics (specifically: time series analysis and econometrics).

Author : A. Bellow,D. Kölzow
Publisher : Springer
Page : 423 pages
File Size : 52,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540381075

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Measure Theory by A. Bellow,D. Kölzow Pdf

Author : Alan Bain,Dan Crisan
Publisher : Springer
Page : 0 pages
File Size : 41,5 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0387568549

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Fundamentals of Stochastic Filtering by Alan Bain,Dan Crisan Pdf

This book provides a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient background to enable study of the recent literature. While no prior knowledge of stochastic filtering is required, readers are assumed to be familiar with measure theory, probability theory and the basics of stochastic processes. Most of the technical results that are required are stated and proved in the appendices. Exercises and solutions are included.

Author : Jie Xiong
Publisher : Oxford University Press on Demand
Page : 285 pages
File Size : 48,5 Mb
Release : 2008-04-17
Category : Business & Economics
ISBN : 9780199219704

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An Introduction to Stochastic Filtering Theory by Jie Xiong Pdf

Stochastic filtering theory is a field that has seen a rapid development in recent years and this book, aimed at graduates and researchers in applied mathematics, provides an accessible introduction covering recent developments.

Author : G. Kallianpur
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 48,5 Mb
Release : 2013-04-17
Category : Science
ISBN : 9781475765922

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Stochastic Filtering Theory by G. Kallianpur Pdf

This book is based on a seminar given at the University of California at Los Angeles in the Spring of 1975. The choice of topics reflects my interests at the time and the needs of the students taking the course. Initially the lectures were written up for publication in the Lecture Notes series. How ever, when I accepted Professor A. V. Balakrishnan's invitation to publish them in the Springer series on Applications of Mathematics it became necessary to alter the informal and often abridged style of the notes and to rewrite or expand much of the original manuscript so as to make the book as self-contained as possible. Even so, no attempt has been made to write a comprehensive treatise on filtering theory, and the book still follows the original plan of the lectures. While this book was in preparation, the two-volume English translation of the work by R. S. Liptser and A. N. Shiryaev has appeared in this series. The first volume and the present book have the same approach to the sub ject, viz. that of martingale theory. Liptser and Shiryaev go into greater detail in the discussion of statistical applications and also consider inter polation and extrapolation as well as filtering.

Author : E. Pap
Publisher : Elsevier
Page : 1632 pages
File Size : 51,6 Mb
Release : 2002-10-31
Category : Mathematics
ISBN : 0080533094

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Handbook of Measure Theory by E. Pap Pdf

The main goal of this Handbook is to survey measure theory with its many different branches and its relations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications which support the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the various areas they contain many special topics and challenging problems valuable for experts and rich sources of inspiration. Mathematicians from other areas as well as physicists, computer scientists, engineers and econometrists will find useful results and powerful methods for their research. The reader may find in the Handbook many close relations to other mathematical areas: real analysis, probability theory, statistics, ergodic theory, functional analysis, potential theory, topology, set theory, geometry, differential equations, optimization, variational analysis, decision making and others. The Handbook is a rich source of relevant references to articles, books and lecture notes and it contains for the reader's convenience an extensive subject and author index.