Smoothing, Filtering and Prediction of Generalized Stochastic Processes
Author: León Abreu (José Luis)
Publisher:
Published: 1970
Total Pages: 188
ISBN-13:
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Stochastic Evolution Systems
Author: Boris L. Rozovsky
Publisher: Springer
Published: 2018-10-03
Total Pages: 340
ISBN-13: 3319948938
DOWNLOAD EBOOKThis 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.
Stochastic Processes and Filtering Theory
Author: Andrew H. Jazwinski
Publisher: Courier Corporation
Published: 2013-04-15
Total Pages: 404
ISBN-13: 0486318192
DOWNLOAD EBOOKThis 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.
Bayesian Filtering and Smoothing
Author: Simo Särkkä
Publisher: Cambridge University Press
Published: 2013-09-05
Total Pages: 255
ISBN-13: 110703065X
DOWNLOAD EBOOKA unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
Nonlinear Filtering and Smoothing
Author: Venkatarama Krishnan
Publisher: Courier Corporation
Published: 2013-10-17
Total Pages: 353
ISBN-13: 0486781836
DOWNLOAD EBOOKMost useful for graduate students in engineering and finance who have a basic knowledge of probability theory, this volume is designed to give a concise understanding of martingales, stochastic integrals, and estimation. It emphasizes applications. Many theorems feature heuristic proofs; others include rigorous proofs to reinforce physical understanding. Numerous end-of-chapter problems enhance the book's practical value. After introducing the basic measure-theoretic concepts of probability and stochastic processes, the text examines martingales, square integrable martingales, and stopping times. Considerations of white noise and white-noise integrals are followed by examinations of stochastic integrals and stochastic differential equations, as well as the associated Ito calculus and its extensions. After defining the Stratonovich integral, the text derives the correction terms needed for computational purposes to convert the Ito stochastic differential equation to the Stratonovich form. Additional chapters contain the derivation of the optimal nonlinear filtering representation, discuss how the Kalman filter stands as a special case of the general nonlinear filtering representation, apply the nonlinear filtering representations to a class of fault-detection problems, and discuss several optimal smoothing representations.
Survey of Linear Optimum Prediction and Smoothing Filters for Nonstationary Stochastic Processes
Author: Andrew Valdis Silinsh
Publisher:
Published: 1963
Total Pages: 128
ISBN-13:
DOWNLOAD EBOOKStatistics of Random Processes II
Author: Robert S. Liptser
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 409
ISBN-13: 3662100282
DOWNLOAD EBOOK"Written by two renowned experts in the field, the books under review contain a thorough and insightful treatment of the fundamental underpinnings of various aspects of stochastic processes as well as a wide range of applications. Providing clear exposition, deep mathematical results, and superb technical representation, they are masterpieces of the subject of stochastic analysis and nonlinear filtering....These books...will become classics." --SIAM REVIEW
Smoothing, Filtering and Prediction
Author: Garry Einicke
Publisher: BoD – Books on Demand
Published: 2012-02-24
Total Pages: 290
ISBN-13: 9533077522
DOWNLOAD EBOOKThis book describes the classical smoothing, filtering and prediction techniques together with some more recently developed embellishments for improving performance within applications. It aims to present the subject in an accessible way, so that it can serve as a practical guide for undergraduates and newcomers to the field. The material is organised as a ten-lecture course. The foundations are laid in Chapters 1 and 2, which explain minimum-mean-square-error solution construction and asymptotic behaviour. Chapters 3 and 4 introduce continuous-time and discrete-time minimum-variance filtering. Generalisations for missing data, deterministic inputs, correlated noises, direct feedthrough terms, output estimation and equalisation are described. Chapter 5 simplifies the minimum-variance filtering results for steady-state problems. Observability, Riccati equation solution convergence, asymptotic stability and Wiener filter equivalence are discussed. Chapters 6 and 7 cover the subject of continuous-time and discrete-time smoothing. The main fixed-lag, fixed-point and fixed-interval smoother results are derived. It is shown that the minimum-variance fixed-interval smoother attains the best performance. Chapter 8 attends to parameter estimation. As the above-mentioned approaches all rely on knowledge of the underlying model parameters, maximum-likelihood techniques within expectation-maximisation algorithms for joint state and parameter estimation are described. Chapter 9 is concerned with robust techniques that accommodate uncertainties within problem specifications. An extra term within Riccati equations enables designers to trade-off average error and peak error performance. Chapter 10 rounds off the course by applying the afore-mentioned linear techniques to nonlinear estimation problems. It is demonstrated that step-wise linearisations can be used within predictors, filters and smoothers, albeit by forsaking optimal performance guarantees.
Statistics of Random Processes
Author: Robert Liptser
Publisher: Springer
Published: 2014-03-12
Total Pages: 427
ISBN-13: 9783662130445
DOWNLOAD EBOOKThese volumes cover non-linear filtering (prediction and smoothing) theory and its applications to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. Also presented is the theory of martingales, of interest to those who deal with problems in financial mathematics. These editions include new material, expanded chapters, and comments on recent progress in the field.
Filtering for Stochastic Processes with Applications to Guidance
Author: Richard S. Bucy
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 238
ISBN-13: 0821837826
DOWNLOAD EBOOKThis 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.''
