Measure Theory And Filtering PDF Download
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| Author | : Lakhdar Aggoun |
| Publisher | : Cambridge University Press |
| Total Pages | : 274 |
| Release | : 2004-09-13 |
| Genre | : Mathematics |
| ISBN | : 9781139456241 |
Download Measure Theory and Filtering Book in PDF, ePub and Kindle
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 |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 395 |
| Release | : 2008-10-08 |
| Genre | : Mathematics |
| ISBN | : 0387768963 |
Download Fundamentals of Stochastic Filtering Book in PDF, ePub and Kindle
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 | : Andrew H. Jazwinski |
| Publisher | : Academic Press |
| Total Pages | : 391 |
| Release | : 1970-01-31 |
| Genre | : Technology & Engineering |
| ISBN | : 0080960901 |
Download Stochastic Processes and Filtering Theory Book in PDF, ePub and Kindle
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 |
| Total Pages | : 292 |
| Release | : 2000 |
| Genre | : Fourier analysis |
| ISBN | : 0953812952 |
Download Measure Theory Book in PDF, ePub and Kindle
| Author | : G. Kallianpur |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 326 |
| Release | : 2013-04-17 |
| Genre | : Science |
| ISBN | : 1475765924 |
Download Stochastic Filtering Theory Book in PDF, ePub and Kindle
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 | : Alan Bain |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2008-11-01 |
| Genre | : Mathematics |
| ISBN | : 9780387568546 |
Download Fundamentals of Stochastic Filtering Book in PDF, ePub and Kindle
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 | : David Williams |
| Publisher | : Cambridge University Press |
| Total Pages | : 274 |
| Release | : 1991-02-14 |
| Genre | : Mathematics |
| ISBN | : 9780521406055 |
Download Probability with Martingales Book in PDF, ePub and Kindle
This is a masterly introduction to the modern, and rigorous, theory of probability. The author emphasises martingales and develops all the necessary measure theory.
| Author | : Jie Xiong |
| Publisher | : Oxford University Press |
| Total Pages | : 285 |
| Release | : 2008-04-17 |
| Genre | : Business & Economics |
| ISBN | : 0199219702 |
Download An Introduction to Stochastic Filtering Theory Book in PDF, ePub and Kindle
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 filteringmodels 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.
| Author | : Donald L. Cohn |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 466 |
| Release | : 2013-07-13 |
| Genre | : Mathematics |
| ISBN | : 1461469562 |
Download Measure Theory Book in PDF, ePub and Kindle
Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings. Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.
| Author | : P.A. Ruymgaart |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 181 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3642968422 |
Download Mathematics of Kalman-Bucy Filtering Book in PDF, ePub and Kindle
Since their introduction in the mid 1950s, the filtering techniques developed by Kalman, and by Kalman and Bucy have been widely known and widely used in all areas of applied sciences. Starting with applications in aerospace engineering, their impact has been felt not only in all areas of engineering but also in the social sciences, biological sciences, medical sciences, as well as all other physical sciences. Despite all the good that has come out of this devel opment, however, there have been misuses because the theory has been used mainly as a tool or a procedure by many applied workers without them fully understanding its underlying mathematical workings. This book addresses a mathematical approach to Kalman-Bucy filtering and is an outgrowth of lectures given at our institutions since 1971 in a sequence of courses devoted to Kalman-Bucy filters. The material is meant to be a theoretical complement to courses dealing with applications and is designed for students who are well versed in the techniques of Kalman-Bucy filtering but who are also interested in the mathematics on which these may be based. The main topic addressed in this book is continuous-time Kalman-Bucy filtering. Although the discrete-time Kalman filter results were obtained first, the continuous-time results are important when dealing with systems developing in time continuously, which are hence more appropriately mod eled by differential equations than by difference equations. On the other hand, observations from the former can be obtained in a discrete fashion.
