An Introduction to Stochastic Filtering Theory


Author: Jie Xiong
Publisher: Oxford University Press on Demand
ISBN: 0199219702
Category: Business & Economics
Page: 270
View: 3200
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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 there are some recent excitingresults in singular filtering models. In this text, Jie Xiong introduces the reader to the basics of Stochastic Filtering Theory before covering the key recent advances. The text is written in a clear style suitable for graduates in mathematics and engineering with a backgroundin basic probability.

Stochastic Partial Differential Equations


Author: Sergey V. Lototsky,Boris L. Rozovsky
Publisher: Springer
ISBN: 3319586475
Category: Mathematics
Page: 508
View: 9416
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Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for time, can move on. Accordingly, no solutions are provided, but there are often hints on how to proceed. The book will be of interest to everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field.

Nonlinear Filtering and Optimal Phase Tracking


Author: Zeev Schuss
Publisher: Springer Science & Business Media
ISBN: 9781461404873
Category: Mathematics
Page: 262
View: 7134
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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.

Stochastic Analysis and Diffusion Processes


Author: Gopinath Kallianpur,P Sundar
Publisher: Oxford University Press
ISBN: 0199657068
Category: Mathematics
Page: 352
View: 1563
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Beginning with the concept of random processes and Brownian motion and building on the theory and research directions in a self-contained manner, this book provides an introduction to stochastic analysis for graduate students, researchers and applied scientists interested in stochastic processes and their applications.

Stochastic Integration in Banach Spaces

Theory and Applications
Author: Vidyadhar Mandrekar,Barbara Rüdiger
Publisher: Springer
ISBN: 3319128531
Category: Mathematics
Page: 211
View: 8137
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Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups. ​

Mathematical Tools for Physicists


Author: Michael Grinfeld
Publisher: John Wiley & Sons
ISBN: 3527684271
Category: Science
Page: 632
View: 3530
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The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Books in Print


Author: R.R. Bowker Company
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 7917
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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual
Author: N.A
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 2819
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Proceedings

Mathematical, physical, and engineering sciences
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Engineering
Page: N.A
View: 3320
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Data Assimilation

A Mathematical Introduction
Author: Kody Law,Andrew Stuart,Konstantinos Zygalakis
Publisher: Springer
ISBN: 3319203258
Category: Mathematics
Page: 242
View: 9395
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This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters. This book is aimed at mathematical researchers interested in a systematic development of this interdisciplinary field, and at researchers from the geosciences, and a variety of other scientific fields, who use tools from data assimilation to combine data with time-dependent models. The numerous examples and illustrations make understanding of the theoretical underpinnings of data assimilation accessible. Furthermore, the examples, exercises and MATLAB software, make the book suitable for students in applied mathematics, either through a lecture course, or through self-study.

Physikalische Berichte


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Physics
Page: N.A
View: 7528
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Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 9954
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Journal of Economic Literature


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Economics
Page: N.A
View: 3876
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Quarterly of Applied Mathematics


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 6097
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American Book Publishing Record

BPR cumulative
Author: N.A
Publisher: N.A
ISBN: N.A
Category: United States
Page: N.A
View: 4280
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JASA


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Statistics
Page: N.A
View: 4780
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Amstat News


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Statistics
Page: N.A
View: 7107
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1089 oder das Wunder der Zahlen

eine Reise in die Welt der Mathematik
Author: David J. Acheson
Publisher: N.A
ISBN: 9783866470200
Category:
Page: 189
View: 6343
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Das Buch beginnt mit einem alten Zaubertrick - Man nehme eine 3-stellige Zahl, etwa 782, kehre sie um, ziehe die kleinere von der größeren ab und addiere dazu die Umkehrung. Also - 782 - 287 = 495, dann 495 + 594. Und schon ist man mitten in der Wunderwelt der Mathematik, denn das Ergebnis ist immer - 1089. Mit solchen und vielen weiteren Beispielen aus Alltag, Geschichte und Wissenschaft gelingt es David Acheson, die faszinierende Welt der Mathematik zu erschließen - ein geistreicher Überblick, eine für jeden verständliche Einführung.

Biometrics


Author: N.A
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 1211
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Kalman-Bucy-Filter

determinist. Beobachtung u. stochast. Filterung
Author: Karl Brammer,Gerhard Siffling
Publisher: N.A
ISBN: N.A
Category: Control theory
Page: 232
View: 6481
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Das Buch will die mannigfaltigen Aufgaben der heutigen Regelungs- und Steuerungstechnik und ihre Lösung nahebringen. Das soll mit möglichst geringem Zeit- und Arbeitsaufwand für den Leser verbunden sein. Leichte Verständlichkeit, Anschaulichkeit und Anwendungsnähe sind deshalb Hauptgesichtspunkt der Darstellung. Vollständigkeit ist nicht angestrebt, vielmehr Darstellung des Wesentlichen. Mathematische Methoden werden auf das Notwendige beschränkt.