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Brownian Motion

Brownian Motion Author Peter Mörters
ISBN-10 9781139486576
Release 2010-03-25
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This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.

Brownian Motion

Brownian Motion Author T. Hida
ISBN-10 9781461260301
Release 2012-12-06
Pages 327
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Following the publication of the Japanese edition of this book, several inter esting developments took place in the area. The author wanted to describe some of these, as well as to offer suggestions concerning future problems which he hoped would stimulate readers working in this field. For these reasons, Chapter 8 was added. Apart from the additional chapter and a few minor changes made by the author, this translation closely follows the text of the original Japanese edition. We would like to thank Professor J. L. Doob for his helpful comments on the English edition. T. Hida T. P. Speed v Preface The physical phenomenon described by Robert Brown was the complex and erratic motion of grains of pollen suspended in a liquid. In the many years which have passed since this description, Brownian motion has become an object of study in pure as well as applied mathematics. Even now many of its important properties are being discovered, and doubtless new and useful aspects remain to be discovered. We are getting a more and more intimate understanding of Brownian motion.

Stochastic Processes

Stochastic Processes Author Richard F. Bass
ISBN-10 9781139501477
Release 2011-10-06
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This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes and semigroup theory. Applications include the Black–Scholes formula for the pricing of derivatives in financial mathematics, the Kalman–Bucy filter used in the US space program and also theoretical applications to partial differential equations and analysis. Short, readable chapters aim for clarity rather than full generality. More than 350 exercises are included to help readers put their new-found knowledge to the test and to prepare them for tackling the research literature.

Brownian Motion

Brownian Motion Author Robert M. Mazo
ISBN-10 9780198515678
Release 2002
Pages 289
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This book describes the theory of how processes on the unobservable molecular scale give rise to observable effects such as diffusion and electrical noise on the macroscopic or laboratory scale. It puts the modern theory into historical context, and features new applications, statistical mechanics derivations, and the mathematical background of the topic.

Long Range Dependence and Self Similarity

Long Range Dependence and Self Similarity Author Vladas Pipiras
ISBN-10 9781107039469
Release 2017-04-18
Pages 382
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A modern and rigorous introduction to long-range dependence and self-similarity, complemented by numerous more specialized up-to-date topics in this research area.

Brownian Models of Performance and Control

Brownian Models of Performance and Control Author J. Michael Harrison
ISBN-10 9781107018396
Release 2013-12-02
Pages 216
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Direct and to the point, this book from one of the field's leaders covers Brownian motion and stochastic calculus at the graduate level, and illustrates the use of that theory in various application domains, emphasizing business and economics. The mathematical development is narrowly focused and briskly paced, with many concrete calculations and a minimum of abstract notation. The applications discussed include: the role of reflected Brownian motion as a storage model, queuing model, or inventory model; optimal stopping problems for Brownian motion, including the influential McDonald–Siegel investment model; optimal control of Brownian motion via barrier policies, including optimal control of Brownian storage systems; and Brownian models of dynamic inference, also called Brownian learning models or Brownian filtering models.


Probability Author Rick Durrett
ISBN-10 9781139491136
Release 2010-08-30
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This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Asymptotic Methods in Stochastics

Asymptotic Methods in Stochastics Author Lajos Horvath and Barbara Szyszkowicz
ISBN-10 082187148X
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Asymptotic Methods in Stochastics has been writing in one form or another for most of life. You can find so many inspiration from Asymptotic Methods in Stochastics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Asymptotic Methods in Stochastics book for free.

Measures Integrals and Martingales

Measures  Integrals and Martingales Author Ren L. Schilling
ISBN-10 9781316620243
Release 2017-04-03
Pages 490
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A concise, elementary introduction to measure and integration theory, requiring few prerequisites as theory is developed quickly and simply.

Brownian Motion

Brownian Motion Author René L. Schilling
ISBN-10 9783110307306
Release 2014-06-18
Pages 424
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Stochastic processes occur everywhere in sciences and engineering, and need to be understood by applied mathematicians, engineers and scientists alike. This is a first course introducing the reader gently to the subject. Brownian motions are a stochastic process, central to many applications and easy to treat.

Probability Random Processes and Statistical Analysis

Probability  Random Processes  and Statistical Analysis Author Hisashi Kobayashi
ISBN-10 9781139502610
Release 2011-12-15
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Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.

Gaussian Processes on Trees

Gaussian Processes on Trees Author Anton Bovier
ISBN-10 9781107160491
Release 2016-10-31
Pages 212
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Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to mean-field spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the F-KPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a self-contained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics.

Financial Engineering and Computation

Financial Engineering and Computation Author Yuh-Dauh Lyuu
ISBN-10 9781139431903
Release 2001-11-12
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Students and professionals intending to work in any area of finance must master not only advanced concepts and mathematical models but also learn how to implement these models computationally. This comprehensive text, first published in 2002, combines the theory and mathematics behind financial engineering with an emphasis on computation, in keeping with the way financial engineering is practised in capital markets. Unlike most books on investments, financial engineering, or derivative securities, the book starts from very basic ideas in finance and gradually builds up the theory. It offers a thorough grounding in the subject for MBAs in finance, students of engineering and sciences who are pursuing a career in finance, researchers in computational finance, system analysts, and financial engineers. Along with the theory, the author presents numerous algorithms for pricing, risk management, and portfolio management. The emphasis is on pricing financial and derivative securities: bonds, options, futures, forwards, interest rate derivatives, mortgage-backed securities, bonds with embedded options, and more.

Classical Potential Theory and Its Probabilistic Counterpart

Classical Potential Theory and Its Probabilistic Counterpart Author Joseph L. Doob
ISBN-10 3540412069
Release 2001-01-12
Pages 846
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From the reviews: "This huge book written in several years by one of the few mathematicians able to do it, appears as a precise and impressive study (not very easy to read) of this bothsided question that replaces, in a coherent way, without being encyclopaedic, a large library of books and papers scattered without a uniform language. Instead of summarizing the author gives his own way of exposition with original complements. This requires no preliminary knowledge. ...The purpose which the author explains in his introduction, i.e. a deep probabilistic interpretation of potential theory and a link between two great theories, appears fulfilled in a masterly manner". M. Brelot in Metrika (1986)

Creating Modern Probability

Creating Modern Probability Author Jan von Plato
ISBN-10 0521597358
Release 1998-01-12
Pages 323
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In this book the author charts the history and development of modern probability theory.

Brownian Motion and Stochastic Calculus

Brownian Motion and Stochastic Calculus Author Ioannis Karatzas
ISBN-10 9781461209492
Release 2014-03-27
Pages 470
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A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.

Topics in Probability and Lie Groups

Topics in Probability and Lie Groups Author John Christopher Taylor
ISBN-10 0821870246
Pages 202
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This volume is comprised of two parts: the first contains articles by S. N. Evans, F. Ledrappier, and Figa-Talomanaca. These articles arose from a Centre de Recherches de Mathematiques (CRM) seminar entitiled, ''Topics in Probability on Lie Groups: Boundary Theory''. Evans gives a synthesis of his pre-1992 work on Gaussian measures on vector spaces over a local field. Ledrappier uses the freegroup on $d$ generators as a paradigm for results on the asymptotic properties of random walks and harmonic measures on the Martin boundary. These articles are followed by a case study by Figa-Talamanca using Gelfand pairs to study a diffusion on a compact ultrametric space. The second part of the book is an appendix to the book Compactifications of Symmetric Spaces (Birkhauser) by Y. Guivarc'h and J. C. Taylor. This appendix consists of an article by each author and presents the contents of this book in a more algebraic way. L. Ji and J.-P. Anker simplifies some of their results on the asymptotics of the Green function that were used to compute Martin boundaries. And Taylor gives a self-contained account of Martin boundary theory for manifolds using the theory of second order strictly elliptic partial differential operators.