• Business & Economics

An Introduction to Stochastic Filtering Theory


Author: Jie Xiong
Publisher: Oxford University Press on Demand
ISBN: 0199219702
Category: Business & Economics
Page: 270
View: 4757
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.

    • Mathematics

Stochastic Analysis and Diffusion Processes


Author: Gopinath Kallianpur,P Sundar
Publisher: Oxford University Press
ISBN: 0199657076
Category: Mathematics
Page: 352
View: 6476
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.

    • Mathematics

Stochastic Partial Differential Equations


Author: Sergey V. Lototsky,Boris L. Rozovsky
Publisher: Springer
ISBN: 3319586475
Category: Mathematics
Page: 508
View: 3591
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.

    • Mathematics

An Introduction to Algebraic Geometry and Algebraic Groups


Author: Meinolf Geck
Publisher: Oxford University Press
ISBN: 019967616X
Category: Mathematics
Page: 320
View: 552
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.

    • Mathematics

Nonlinear Filtering and Optimal Phase Tracking


Author: Zeev Schuss
Publisher: Springer Science & Business Media
ISBN: 9781461404873
Category: Mathematics
Page: 262
View: 5920
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.

    • Business & Economics

Stochastic Integration Theory


Author: Peter Medvegyev
Publisher: Oxford University Press on Demand
ISBN: 0199215251
Category: Business & Economics
Page: 608
View: 5210
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).

    • Mathematics

Stochastic Analysis and Diffusion Processes


Author: Gopinath Kallianpur,P Sundar
Publisher: Oxford University Press
ISBN: 0199657076
Category: Mathematics
Page: 352
View: 7322
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.

    • Business & Economics

Stochastic Limit Theory

An Introduction for Econometricians
Author: James Davidson
Publisher: Oxford University Press
ISBN: 0198774036
Category: Business & Economics
Page: 539
View: 3917
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.

    • Mathematics

An Introduction to Random Matrices


Author: Greg W. Anderson,Alice Guionnet,Ofer Zeitouni
Publisher: Cambridge University Press
ISBN: 0521194520
Category: Mathematics
Page: 492
View: 7757
A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

    • Mathematics

Algebraic Models in Geometry


Author: Yves Félix,John Oprea,Daniel Tanré
Publisher: Oxford University Press
ISBN: 0199206511
Category: Mathematics
Page: 460
View: 4245
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.

    • Mathematics

Markov Chains


Author: J. R. Norris
Publisher: Cambridge University Press
ISBN: 1107393477
Category: Mathematics
Page: N.A
View: 7291
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.

    • Mathematics

Probability with Martingales


Author: David Williams
Publisher: Cambridge University Press
ISBN: 1139642987
Category: Mathematics
Page: N.A
View: 7320
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.

    • Science

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: 7458
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.

    • Mathematics

Brownian Motion, Martingales, and Stochastic Calculus


Author: Jean-François Le Gall
Publisher: Springer
ISBN: 3319310895
Category: Mathematics
Page: 273
View: 1197
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.

    • Mathematics

Pattern Theory

The Stochastic Analysis of Real-World Signals
Author: David Mumford,Agnès Desolneux
Publisher: CRC Press
ISBN: 1439865566
Category: Mathematics
Page: 375
View: 4707
Pattern theory is a distinctive approach to the analysis of all forms of real-world signals. At its core is the design of a large variety of probabilistic models whose samples reproduce the look and feel of the real signals, their patterns, and their variability. Bayesian statistical inference then allows you to apply these models in the analysis of new signals. This book treats the mathematical tools, the models themselves, and the computational algorithms for applying statistics to analyze six representative classes of signals of increasing complexity. The book covers patterns in text, sound, and images. Discussions of images include recognizing characters, textures, nature scenes, and human faces. The text includes online access to the materials (data, code, etc.) needed for the exercises.

    • Mathematics

Algebraic Geometry and Arithmetic Curves


Author: Qing Liu,Reinie Erne
Publisher: Oxford University Press
ISBN: 0191547808
Category: Mathematics
Page: 592
View: 5222
This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.

    • Mathematics

Large Deviations


Author: Frank den Hollander
Publisher: American Mathematical Soc.
ISBN: 9780821844359
Category: Mathematics
Page: 146
View: 2821
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.

    • Banach algebras

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: 4372
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).

    • Mathematics

4-Manifolds


Author: Selman Akbulut
Publisher: Oxford University Press
ISBN: 0191087769
Category: Mathematics
Page: 280
View: 7429
This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut. The text is aimed at graduate students and focuses on the teaching and learning of the subject, giving a direct approach to constructions and theorems which are supplemented by exercises to help the reader work through the details not covered in the proofs. The book contains a hundred colour illustrations to demonstrate the ideas rather than providing long-winded and potentially unclear explanations. Key results have been selected that relate to the material discussed and the author has provided examples of how to analyse them with the techniques developed in earlier chapters.

    • Mathematics

Introduction To Commutative Algebra


Author: Michael Atiyah
Publisher: CRC Press
ISBN: 0429973268
Category: Mathematics
Page: 140
View: 5213
First Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company.