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This book provides a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods.
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The objective of stochastic filtering is to determine the best estimate for the state of a stochastic dynamical system from partial observations. The solution of this problem in the linear case is the well known Kalman-Bucy filter which has found widespread practical application. The purpose of this book is to provide 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.
The book is intended as a reference for graduate students and researchers interested in the field. It is also suitable for use as a text for a graduate level course on stochastic filtering. Suitable exercises and solutions are included.
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“This book provides a rigorous mathematical treatment of the nonlinear stochastic filtering problem with particular emphasis on numerical methods. ... The text is essentially self-contained ... . In an appendice the required results from measure theory and stochastic analysis are stated and proved. Intended readers are researchers and graduate students that have an interest in theoretical aspects of stochastic filtering. The text is supplemented with many exercises and detailed solutions. ... a standard reference for teaching and working in the field of stochastic filtering.” (H. M. Mai, Zentralblatt MATH, Vol. 1176, 2010)
“This book is one of the few books dealing with both the theoretical foundations and modern stochastic particle techniques in stochastic filtering through the entire text. ... I highly recommend this book to any researcher in applied mathematics, as well as to any researchers in engineering and computer sciences with some background in statistics and probability. ... The book can also serve as a useful text for an informal seminar or a second year graduate course on stochastic filtering.” (Pierre Del Moral, Bulletin of the American Mathematical Society, Vol. 48 (2), April, 2011)
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- PublisherSpringer
- Publication date2010
- ISBN 10 1441926429
- ISBN 13 9781441926425
- BindingPaperback
- Number of pages403
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Fundamentals of Stochastic Filtering
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Book Description Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Many aspects of phenomena critical to our lives can not be measured directly. Fortunately models of these phenomena, together with more limited obs- vations frequently allow us to make reasonable inferences about the state of the systems that a ect us. The process of using partial observations and a stochastic model to make inferences about an evolving system is known as stochastic ltering. The objective of this text is to assist anyone who would like to become familiar with the theory of stochastic ltering, whether graduate student or more experienced scientist. The majority of the fundamental results of the subject are presented using modern methods making them readily available for reference. The book may also be of interest to practitioners of stochastic ltering, who wish to gain a better understanding of the underlying theory. Stochastic ltering in continuous time relies heavily on measure theory, stochasticprocessesandstochasticcalculus.Whileknowledgeofbasicmeasure theory and probability is assumed, the text is largely self-contained in that the majority of the results needed are stated in two appendices. This should make it easy for the book to be used as a graduate teaching text. With this in mind, each chapter contains a number of exercises, with solutions detailed at the end of the chapter. 404 pp. Englisch. Seller Inventory # 9781441926425
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Book Description Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. The authors are an authority in the stochastic filtering fieldAn assortment of Measure Theory, Probability Theory and Stochastic Analysis results are included in order to make this book as self contained as possibleExercises and solutions i. Seller Inventory # 4173146
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