An Introduction to Stochastic Filtering Theory


Author: Jie Xiong
Publisher: Oxford University Press on Demand
ISBN: 0199219702
Category: Business & Economics
Page: 270
View: 6861
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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 Analysis and Diffusion Processes


Author: Gopinath Kallianpur,P Sundar
Publisher: Oxford University Press
ISBN: 0199657076
Category: Mathematics
Page: 352
View: 4178
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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 Theory


Author: Peter Medvegyev
Publisher: Oxford University Press on Demand
ISBN: 0199215251
Category: Business & Economics
Page: 608
View: 4504
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This graduate level text covers the theory of stochastic integration, an important area of Mathematics that has a wide range of applications, including financial mathematics and signal processing. Aimed at graduate students in Mathematics, Statistics, Probability, Mathematical Finance, and Economics, the book not only covers the theory of the stochastic integral in great depth but also presents the associated theory (martingales, Levy processes) and important examples (Brownianmotion, Poisson process).

Stochastic Partial Differential Equations


Author: Sergey V. Lototsky,Boris L. Rozovsky
Publisher: Springer
ISBN: 3319586475
Category: Mathematics
Page: 508
View: 1903
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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.

An Introduction to Algebraic Geometry and Algebraic Groups


Author: Meinolf Geck
Publisher: Oxford University Press
ISBN: 019967616X
Category: Mathematics
Page: 320
View: 6779
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An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.

Nonlinear Filtering and Optimal Phase Tracking


Author: Zeev Schuss
Publisher: Springer Science & Business Media
ISBN: 9781461404873
Category: Mathematics
Page: 262
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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: 0199657076
Category: Mathematics
Page: 352
View: 8018
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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 Limit Theory

An Introduction for Econometricians
Author: James Davidson
Publisher: Oxford University Press
ISBN: 0198774036
Category: Business & Economics
Page: 539
View: 2082
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This is a survey of the recent developments in the rapidly expanding field of asymptotic distribution theory, with a special emphasis on the problems of time dependence and heterogeneity. The book is designed to be useful on two levels. First as a textbook and reference work, giving definitions of the relevant mathematical concepts, statements, and proofs of the important results from the probability literature, and numerous examples; and second, as an account of recent work in thefield of particular interest to econometricians, including a number of important new results. It is virtually self-contained, with all but the most basic technical prerequisites being explained in their context; mathematical topics include measure theory, integration, metric spaces, and topology, with applications to random variables, and an extended treatment of conditional probability. Other subjects treated include: stochastic processes, mixing processes, martingales, mixingales, and near-epoch dependence; the weak and strong laws of large numbers; weak convergence; and central limit theorems for nonstationary and dependent processes. The functional central limit theorem and its ramifications are covered in detail, including an account of the theoretical underpinnings (the weak convergence of measures on metric spaces), Brownian motion, the multivariate invariance principle, and convergence to stochastic integrals. This material is of special relevance to the theory of cointegration.

Introduction to Symplectic Topology


Author: Dusa McDuff,Dietmar Salamon
Publisher: Oxford University Press
ISBN: 0192514016
Category: Mathematics
Page: 632
View: 3046
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Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. A significantly revised second edition was published in 1998 introducing new sections and updates on the fast-developing area. This new third edition includes updates and new material to bring the book right up-to-date.

Markov Chains


Author: J. R. Norris
Publisher: Cambridge University Press
ISBN: 1107393477
Category: Mathematics
Page: N.A
View: 4086
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Markov chains are central to the understanding of random processes. This is not only because they pervade the applications of random processes, but also because one can calculate explicitly many quantities of interest. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov chains and quickly develops a coherent and rigorous theory whilst showing also how actually to apply it. Both discrete-time and continuous-time chains are studied. A distinguishing feature is an introduction to more advanced topics such as martingales and potentials in the established context of Markov chains. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and exercises and examples drawn both from theory and practice. It will therefore be an ideal text either for elementary courses on random processes or those that are more oriented towards applications.

Markov Processes

An Introduction for Physical Scientists
Author: Daniel T. Gillespie
Publisher: Gulf Professional Publishing
ISBN: 9780122839559
Category: Mathematics
Page: 565
View: 6004
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Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level. A self-contained, prgamatic exposition of the needed elements of random variable theory Logically integrated derviations of the Chapman-Kolmogorov equation, the Kramers-Moyal equations, the Fokker-Planck equations, the Langevin equation, the master equations, and the moment equations Detailed exposition of Monte Carlo simulation methods, with plots of many numerical examples Clear treatments of first passages, first exits, and stable state fluctuations and transitions Carefully drawn applications to Brownian motion, molecular diffusion, and chemical kinetics

Introduction to Modern Analysis


Author: Shmuel Kantorovitz
Publisher: Oxford University Press on Demand
ISBN: 0198526563
Category: Psychology
Page: 434
View: 6784
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This text is based on lectures given by the author at the advanced undergraduate and graduate levels in Measure Theory, Functional Analysis, Banach Algebras, Spectral Theory (of bounded and unbounded operators), Semigroups of Operators, Probability and Mathematical Statistics, and Partial Differential Equations. The first 10 chapters discuss theoretical methods in Measure Theory and Functional Analysis, and contain over 120 end of chapter exercises. The final two chapters apply theory toapplications in Probability Theory and Partial Differential Equations. The Measure Theory chapters discuss the Lebesgue-Radon-Nikodym theorem which is given the Von Neumann Hilbert space proof. Also included are the relatively advanced topics of Haar measure, differentiability of complex Borel measures in Euclidean space with respect to Lebesgue measure, and the Marcinkiewicz' interpolation theorem for operators between Lebesgue spaces. The Functional Analysis chapters cover the usual material on Banach spaces, weak topologies, separation, extremal points, the Stone-Weierstrass theorem, Hilbert spaces, Banach algebras, and Spectral Theory for both bounded and unbounded operators. Relatively advanced topics such as the Gelfand-Naimark-Segal representation theorem and the Von Neumann double commutant theorem are included. The final two chapters deal with applications, where the measure theory and functional analysis methods of the first ten chapters are applied to ProbabilityTheory and the Theory of Distributions and PDE's. Again, some advanced topics are included, such as the Lyapounov Central Limit theorem, the Kolmogoroff "Three Series theorem", the Ehrenpreis-Malgrange-Hormander theorem on fundamental solutions, and Hormander's theory of convolution operators. The Oxford Graduate Texts in Mathematics series aim is to publish textbooks suitable for graduate students in mathematics and its applications. The level of books may range from some suitable for advanced undergraduate courses at one end, to others of interest to research workers. The emphasis is on texts of high mathematical quality in active areas, particularly areas that are not well represented in the literature at present.

Algebraic Models in Geometry


Author: Yves Félix,John Oprea,Daniel Tanré
Publisher: Oxford University Press
ISBN: 0199206511
Category: Mathematics
Page: 460
View: 5780
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In the past century, different branches of mathematics have become more widely separated. Yet, there is an essential unity to mathematics which still springs up in fascinating ways to solve interdisciplinary problems. This text provides a bridge between the subjects of algebraic topology, including differential topology, and geometry. It is a survey book dedicated to a large audience of researchers and graduate students in these areas. Containing a generalintroduction to the algebraic theory of rational homotopy and giving concrete applications of algebraic models to the study of geometrical problems, mathematicians in many areas will find subjects that are of interest to them in the book.

An Introduction to Random Matrices


Author: Greg W. Anderson,Alice Guionnet,Ofer Zeitouni
Publisher: Cambridge University Press
ISBN: 0521194520
Category: Mathematics
Page: 492
View: 5844
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A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

Arbitrage Theory in Continuous Time


Author: Tomas Björk
Publisher: OUP Oxford
ISBN: 0191610291
Category: Business & Economics
Page: 560
View: 6257
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The third edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. In this substantially extended new edition Bjork has added separate and complete chapters on the martingale approach to optimal investment problems, optimal stopping theory with applications to American options, and positive interest models and their connection to potential theory and stochastic discount factors. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.

Chemical Dynamics in Condensed Phases

Relaxation, Transfer and Reactions in Condensed Molecular Systems
Author: Abraham Nitzan
Publisher: Oxford University Press
ISBN: 0198529791
Category: Science
Page: 719
View: 5830
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Graduate level textbook presenting some of the most fundamental processes that underlie physical, chemical and biological phenomena in complex condensed phase systems. Includes in-depth descriptions of relevant methodologies, and provides ample introductory material for readers of different backgrounds.

Probability with Martingales


Author: David Williams
Publisher: Cambridge University Press
ISBN: 1139642987
Category: Mathematics
Page: N.A
View: 5357
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Probability theory is nowadays applied in a huge variety of fields including physics, engineering, biology, economics and the social sciences. This book is a modern, lively and rigorous account which has Doob's theory of martingales in discrete time as its main theme. It proves important results such as Kolmogorov's Strong Law of Large Numbers and the Three-Series Theorem by martingale techniques, and the Central Limit Theorem via the use of characteristic functions. A distinguishing feature is its determination to keep the probability flowing at a nice tempo. It achieves this by being selective rather than encyclopaedic, presenting only what is essential to understand the fundamentals; and it assumes certain key results from measure theory in the main text. These measure-theoretic results are proved in full in appendices, so that the book is completely self-contained. The book is written for students, not for researchers, and has evolved through several years of class testing. Exercises play a vital rôle. Interesting and challenging problems, some with hints, consolidate what has already been learnt, and provide motivation to discover more of the subject than can be covered in a single introduction.

Large Deviations


Author: Frank den Hollander
Publisher: American Mathematical Soc.
ISBN: 9780821844359
Category: Mathematics
Page: 146
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This book is an introduction to the theory and applications of large deviations, a branch of probability theory that describes the probability of rare events in terms of variational problems. By focusing the theory, in Part A of the book, on random sequences, the author succeeds in conveying the main ideas behind large deviations without a need for technicalities, thus providing a concise and accessible entry to this challenging and captivating subject. The selection of modern applications, described in Part B of the book, offers a good sample of what large deviation theory is able to achieve in various different contexts: statistical hypothesis testing, random walk in random environment, heat conduction with random sources and sinks, polymer chains, and interacting diffusions. With its 60 exercises and solutions, this book can be used as a text for graduate students who have had some exposure to mathematical analysis and measure-theoretic probability.

Introduction to Banach Spaces and Algebras


Author: Graham R. Allan,Harold G. Dales
Publisher: Oxford University Press
ISBN: 0199206538
Category: Banach algebras
Page: 371
View: 474
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A graduate level text in functional analysis, with an emphasis on Banach algebras. Based on lectures given for Part III of the Cambridge Mathematical Tripos, the text will assume a familiarity with elementary real and complex analysis, and some acquaintance with metric spaces, analytic topology and normed spaces (but not theorems depending on Baire category, or any version of the Hahn-Banach theorem).

Introduction To Commutative Algebra


Author: Michael Atiyah
Publisher: CRC Press
ISBN: 0429973268
Category: Mathematics
Page: 140
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First Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company.