Stochastic Filtering Theory

Author : G. Kallianpur
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 50,7 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 : Jie Xiong
Publisher : Oxford University Press on Demand
Page : 285 pages
File Size : 48,6 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 : Andrew H. Jazwinski
Publisher : Courier Corporation
Page : 404 pages
File Size : 53,7 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 : Alan Bain,Dan Crisan
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 44,5 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 : Boris L. Rozovsky,Sergey V. Lototsky
Publisher : Springer
Page : 330 pages
File Size : 55,9 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9783319948935

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Stochastic Evolution Systems by Boris L. Rozovsky,Sergey V. Lototsky Pdf

This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.

Author : Ramaprasad Bhar
Publisher : World Scientific
Page : 354 pages
File Size : 52,6 Mb
Release : 2010
Category : Business & Economics
ISBN : 9789814304856

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Stochastic Filtering with Applications in Finance by Ramaprasad Bhar Pdf

This book provides a comprehensive account of stochastic filtering as a modeling tool in finance and economics. It aims to present this very important tool with a view to making it more popular among researchers in the disciplines of finance and economics. It is not intended to give a complete mathematical treatment of different stochastic filtering approaches, but rather to describe them in simple terms and illustrate their application with real historical data for problems normally encountered in these disciplines. Beyond laying out the steps to be implemented, the steps are demonstrated in the context of different market segments. Although no prior knowledge in this area is required, the reader is expected to have knowledge of probability theory as well as a general mathematical aptitude. Its simple presentation of complex algorithms required to solve modeling problems in increasingly sophisticated financial markets makes this book particularly valuable as a reference for graduate students and researchers interested in the field. Furthermore, it analyses the model estimation results in the context of the market and contrasts these with contemporary research publications. It is also suitable for use as a text for graduate level courses on stochastic modeling.

Author : Rong SITU
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 55,7 Mb
Release : 2006-05-06
Category : Technology & Engineering
ISBN : 9780387251752

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Theory of Stochastic Differential Equations with Jumps and Applications by Rong SITU Pdf

Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.

Author : Pierre Del Moral,Spiridon Penev
Publisher : CRC Press
Page : 866 pages
File Size : 40,9 Mb
Release : 2017-02-24
Category : Mathematics
ISBN : 9781498701846

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Stochastic Processes by Pierre Del Moral,Spiridon Penev Pdf

Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.

Author : Mohinder S. Grewal,Angus P. Andrews
Publisher : John Wiley & Sons
Page : 640 pages
File Size : 47,5 Mb
Release : 2015-02-02
Category : Technology & Engineering
ISBN : 9781118984963

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Kalman Filtering by Mohinder S. Grewal,Angus P. Andrews Pdf

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.

Author : Harold Kushner
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461244820

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Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems by Harold Kushner Pdf

The book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).

Author : A. V. Balakrishnan
Publisher : Unknown
Page : 128 pages
File Size : 41,5 Mb
Release : 1973
Category : Control theory
ISBN : 038706303X

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Lecture Notes in Economics and Mathematical Systems by A. V. Balakrishnan Pdf

Author : Lifeng Ma,Zidong Wang,Yuming Bo
Publisher : CRC Press
Page : 180 pages
File Size : 55,6 Mb
Release : 2018-12-07
Category : Technology & Engineering
ISBN : 9780429761928

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Nonlinear Control and Filtering for Stochastic Networked Systems by Lifeng Ma,Zidong Wang,Yuming Bo Pdf

In this book, control and filtering problems for several classes of stochastic networked systems are discussed. In each chapter, the stability, robustness, reliability, consensus performance, and/or disturbance attenuation levels are investigated within a unified theoretical framework. The aim is to derive the sufficient conditions such that the resulting systems achieve the prescribed design requirements despite all the network-induced phenomena. Further, novel notions such as randomly occurring sensor failures and consensus in probability are discussed. Finally, the theories/techniques developed are applied to emerging research areas. Key Features Unifies existing and emerging concepts concerning stochastic control/filtering and distributed control/filtering with an emphasis on a variety of network-induced complexities Includes concepts like randomly occurring sensor failures and consensus in probability (with respect to time-varying stochastic multi-agent systems) Exploits the recursive linear matrix inequality approach, completing the square method, Hamilton-Jacobi inequality approach, and parameter-dependent matrix inequality approach to handle the emerging mathematical/computational challenges Captures recent advances of theories, techniques, and applications of stochastic control as well as filtering from an engineering-oriented perspective Gives simulation examples in each chapter to reflect the engineering practice

Author : Georg Lindgren
Publisher : CRC Press
Page : 378 pages
File Size : 41,5 Mb
Release : 2012-10-01
Category : Mathematics
ISBN : 9781466557796

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Stationary Stochastic Processes by Georg Lindgren Pdf

Intended for a second course in stationary processes, Stationary Stochastic Processes: Theory and Applications presents the theory behind the field’s widely scattered applications in engineering and science. In addition, it reviews sample function properties and spectral representations for stationary processes and fields, including a portion on stationary point processes. Features Presents and illustrates the fundamental correlation and spectral methods for stochastic processes and random fields Explains how the basic theory is used in special applications like detection theory and signal processing, spatial statistics, and reliability Motivates mathematical theory from a statistical model-building viewpoint Introduces a selection of special topics, including extreme value theory, filter theory, long-range dependence, and point processes Provides more than 100 exercises with hints to solutions and selected full solutions This book covers key topics such as ergodicity, crossing problems, and extremes, and opens the doors to a selection of special topics, like extreme value theory, filter theory, long-range dependence, and point processes, and includes many exercises and examples to illustrate the theory. Precise in mathematical details without being pedantic, Stationary Stochastic Processes: Theory and Applications is for the student with some experience with stochastic processes and a desire for deeper understanding without getting bogged down in abstract mathematics.

Author : Lakhdar Aggoun,Robert J. Elliott
Publisher : Cambridge University Press
Page : 274 pages
File Size : 43,7 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 : Richard S. Bucy,Peter D. Joseph
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 43,8 Mb
Release : 2005
Category : Mathematics
ISBN : 0821837826

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Filtering for Stochastic Processes with Applications to Guidance by Richard S. Bucy,Peter D. Joseph Pdf

This second edition preserves the original text of 1968, with clarification and added references. From the Preface to the Second Edition: ``Since the First Edition of this book, numerous important results have appeared--in particular stochastic integrals with respect to martingales, random fields, Riccati equation theory and realization of nonlinear filters, to name a few. In Appendix D, an attempt is made to provide some of the references that the authors have found useful and tocomment on the relation of the cited references to the field ... [W]e hope that this new edition will have the effect of hastening the day when the nonlinear filter will enjoy the same popularity in applications as the linear filter does now.''