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Measure Theory And Filtering
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Book Synopsis Measure Theory and Filtering by : Lakhdar Aggoun
Download or read book Measure Theory and Filtering written by Lakhdar Aggoun and published by Cambridge University Press. This book was released on 2004-09-13 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fundamentals of Stochastic Filtering by : Alan Bain
Download or read book Fundamentals of Stochastic Filtering written by Alan Bain and published by Springer Science & Business Media. This book was released on 2008-10-08 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Processes and Filtering Theory by : Andrew H. Jazwinski
Download or read book Stochastic Processes and Filtering Theory written by Andrew H. Jazwinski and published by Courier Corporation. This book was released on 2013-04-15 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Probability with Martingales by : David Williams
Download or read book Probability with Martingales written by David Williams and published by Cambridge University Press. This book was released on 1991-02-14 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a masterly introduction to the modern, and rigorous, theory of probability. The author emphasises martingales and develops all the necessary measure theory.
Book Synopsis Bayesian Filtering and Smoothing by : Simo Särkkä
Download or read book Bayesian Filtering and Smoothing written by Simo Särkkä and published by Cambridge University Press. This book was released on 2013-09-05 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
Book Synopsis A User's Guide to Measure Theoretic Probability by : David Pollard
Download or read book A User's Guide to Measure Theoretic Probability written by David Pollard and published by Cambridge University Press. This book was released on 2002 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.
Book Synopsis Probability Theory by : S. R. S. Varadhan
Download or read book Probability Theory written by S. R. S. Varadhan and published by American Mathematical Soc.. This book was released on 2001-09-10 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences. The necessary background material in measure theory is developed, including the standard topics, such as extension theorem, construction of measures, integration, product spaces, Radon-Nikodym theorem, and conditional expectation. In the first part of the book, characteristic functions are introduced, followed by the study of weak convergence of probability distributions. Then both the weak and strong limit theorems for sums of independent random variables are proved, including the weak and strong laws of large numbers, central limit theorems, laws of the iterated logarithm, and the Kolmogorov three series theorem. The first part concludes with infinitely divisible distributions and limit theorems for sums of uniformly infinitesimal independent random variables. The second part of the book mainly deals with dependent random variables, particularly martingales and Markov chains. Topics include standard results regarding discrete parameter martingales and Doob's inequalities. The standard topics in Markov chains are treated, i.e., transience, and null and positive recurrence. A varied collection of examples is given to demonstrate the connection between martingales and Markov chains. Additional topics covered in the book include stationary Gaussian processes, ergodic theorems, dynamic programming, optimal stopping, and filtering. A large number of examples and exercises is included. The book is a suitable text for a first-year graduate course in probability.
Book Synopsis Kalman Filtering by : Mohinder S. Grewal
Download or read book Kalman Filtering written by Mohinder S. Grewal and published by John Wiley & Sons. This book was released on 2015-02-02 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive textbook and professional reference on Kalman Filtering – fully updated, revised, and expanded This book contains the latest developments in the implementation and application of Kalman filtering. Authors Grewal and Andrews draw upon their decades of experience to offer an in-depth examination of the subtleties, common pitfalls, and limitations of estimation theory as it applies to real-world situations. They present many illustrative examples including adaptations for nonlinear filtering, global navigation satellite systems, the error modeling of gyros and accelerometers, inertial navigation systems, and freeway traffic control. Kalman Filtering: Theory and Practice Using MATLAB, Fourth Edition is an ideal textbook in advanced undergraduate and beginning graduate courses in stochastic processes and Kalman filtering. It is also appropriate for self-instruction or review by practicing engineers and scientists who want to learn more about this important topic.
Book Synopsis Optimal Filtering by : Brian D. O. Anderson
Download or read book Optimal Filtering written by Brian D. O. Anderson and published by Courier Corporation. This book was released on 2012-05-23 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text extends studies of signal processing, particularly regarding communication systems and digital filtering theory. Topics include filtering, linear systems, and estimation; discrete-time Kalman filter; time-invariant filters; more. 1979 edition.
Book Synopsis Random Finite Sets for Robot Mapping & SLAM by : John Stephen Mullane
Download or read book Random Finite Sets for Robot Mapping & SLAM written by John Stephen Mullane and published by Springer Science & Business Media. This book was released on 2011-05-19 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph written by John Mullane, Ba-Ngu Vo, Martin Adams and Ba-Tuong Vo is devoted to the field of autonomous robot systems, which have been receiving a great deal of attention by the research community in the latest few years. The contents are focused on the problem of representing the environment and its uncertainty in terms of feature based maps. Random Finite Sets are adopted as the fundamental tool to represent a map, and a general framework is proposed for feature management, data association and state estimation. The approaches are tested in a number of experiments on both ground based and marine based facilities.
Book Synopsis Stochastic Processes for Physicists by : Kurt Jacobs
Download or read book Stochastic Processes for Physicists written by Kurt Jacobs and published by Cambridge University Press. This book was released on 2010-02-18 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics.
Book Synopsis An Introduction to Stochastic Filtering Theory by : Jie Xiong
Download or read book An Introduction to Stochastic Filtering Theory written by Jie Xiong and published by OUP Oxford. This book was released on 2008-04-17 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Filtering Theory uses probability tools to estimate unobservable stochastic processes that arise in many applied fields including communication, target-tracking, and mathematical finance. As a topic, Stochastic Filtering Theory has progressed rapidly in recent years. For example, the (branching) particle system representation of the optimal filter has been extensively studied to seek more effective numerical approximations of the optimal filter; the stability of the filter with "incorrect" initial state, as well as the long-term behavior of the optimal filter, has attracted the attention of many researchers; and although still in its infancy, the study of singular filtering models has yielded exciting results. In this text, Jie Xiong introduces the reader to the basics of Stochastic Filtering Theory before covering these key recent advances. The text is written in a style suitable for graduates in mathematics and engineering with a background in basic probability.
Book Synopsis State Estimation for Nonlinear Continuous–Discrete Stochastic Systems by : Gennady Yu. Kulikov
Download or read book State Estimation for Nonlinear Continuous–Discrete Stochastic Systems written by Gennady Yu. Kulikov and published by Springer Nature. This book was released on with total page 813 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Filtering and Optimal Phase Tracking by : Zeev Schuss
Download or read book Nonlinear Filtering and Optimal Phase Tracking written by Zeev Schuss and published by Springer Science & Business Media. This book was released on 2011-11-16 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an analytical rather than measure-theoretical approach to the derivation of the partial differential equations of nonlinear filtering theory. The basis for this approach is the discrete numerical scheme used in Monte-Carlo simulations of stochastic differential equations and Wiener's associated path integral representation of the transition probability density. Furthermore, it presents analytical methods for constructing asymptotic approximations to their solution and for synthesizing asymptotically optimal filters. It also offers a new approach to the phase tracking problem, based on optimizing the mean time to loss of lock. The book is based on lecture notes from a one-semester special topics course on stochastic processes and their applications that the author taught many times to graduate students of mathematics, applied mathematics, physics, chemistry, computer science, electrical engineering, and other disciplines. The book contains exercises and worked-out examples aimed at illustrating the methods of mathematical modeling and performance analysis of phase trackers.
Book Synopsis Adaptive Filtering Prediction and Control by : Graham C Goodwin
Download or read book Adaptive Filtering Prediction and Control written by Graham C Goodwin and published by Courier Corporation. This book was released on 2014-05-05 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unified survey focuses on linear discrete-time systems and explores natural extensions to nonlinear systems. It emphasizes discrete-time systems, summarizing theoretical and practical aspects of a large class of adaptive algorithms. 1984 edition.
Book Synopsis Stochastic Calculus and Applications by : Samuel N. Cohen
Download or read book Stochastic Calculus and Applications written by Samuel N. Cohen and published by Birkhäuser. This book was released on 2015-11-18 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."–Zentralblatt (from review of the First Edition)
Book Synopsis Kalman Filtering by : Mohinder S. Grewal
Download or read book Kalman Filtering written by Mohinder S. Grewal and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with a solid introduction to the theoretical and practical aspects of Kalman filtering. It has been updated with the latest developments in the implementation and application of Kalman filtering, including adaptations for nonlinear filtering, more robust smoothing methods, and developing applications in navigation. All software is provided in MATLAB, giving readers the opportunity to discover how the Kalman filter works in action and to consider the practical arithmetic needed to preserve the accuracy of results. Note: CD-ROM/DVD and other supplementary materials are not included as part of eBook file. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department -- to obtain the manual, send an email to [email protected].
