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Graduate Texts in Mathematics Ser.: Brownian Motion and Stochastic Calculus by Ioannis Karatzas and Steven E. Shreve (1991, Trade Paperback)

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Brownian Motion and Stochastic Calculus, Paperback by Karatzas, Ioannis; Shreve, Steve E. (EDT), ISBN 0387976558, ISBN-13 9780387976556, Brand New, Free shipping in the US For readers familiar with measure-theoretic probability and discrete time processes, who wish to explore stochastic processes in continuous time. Annotation copyright Book News, Inc. Portland, Or.

About this product

Product Identifiers

PublisherSpringer New York

ISBN-100387976558

ISBN-139780387976556

eBay Product ID (ePID)126094

Product Key Features

Number of PagesXxiii, 470 Pages

Publication NameBrownian Motion and Stochastic Calculus

LanguageEnglish

Publication Year1991

SubjectProbability & Statistics / Stochastic Processes, Mechanics / General, Probability & Statistics / General, Chemistry / General

FeaturesRevised

TypeTextbook

AuthorIoannis Karatzas, Steven E. Shreve

Subject AreaMathematics, Science

SeriesGraduate Texts in Mathematics Ser.

FormatTrade Paperback

Dimensions

Item Height0.4 in

Item Weight53.6 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Edition Number2

Intended AudienceScholarly & Professional

LCCN96-167783

Dewey Edition21

ReviewsSecond EditionI. Karatzas and S.E. ShreveBrownian Motion and Stochastic Calculus"A valuable book for every graduate student studying stochastic process, and for those who are interested in pure and applied probability. The authors have done a good job."-MATHEMATICAL REVIEWS, Second Edition I. Karatzas and S.E. Shreve Brownian Motion and Stochastic Calculus "A valuable book for every graduate student studying stochastic process, and for those who are interested in pure and applied probability. The authors have done a good job."--MATHEMATICAL REVIEWS, Second Edition I. Karatzas and S.E. Shreve Brownian Motion and Stochastic Calculus "A valuable book for every graduate student studying stochastic process, and for those who are interested in pure and applied probability. The authors have done a good job."-MATHEMATICAL REVIEWS, Second Edition I. Karatzas and S.E. Shreve Brownian Motion and Stochastic Calculus "A valuable book for every graduate student studying stochastic process, and for those who are interested in pure and applied probability. The authors have done a good job."a? MATHEMATICAL REVIEWS

Series Volume Number113

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal530.4/75

Edition DescriptionRevised edition

Table Of Content1 Martingales, Stopping Times, and Filtrations.- 1.1. Stochastic Processes and ?-Fields.- 1.2. Stopping Times.- 1.3. Continuous-Time Martingales.- 1.4. The Doob--Meyer Decomposition.- 1.5. Continuous, Square-Integrable Martingales.- 1.6. Solutions to Selected Problems.- 1.7. Notes.- 2 Brownian Motion.- 2.1. Introduction.- 2.2. First Construction of Brownian Motion.- 2.3. Second Construction of Brownian Motion.- 2.4. The SpaceC[0, ?), Weak Convergence, and Wiener Measure.- 2.5. The Markov Property.- 2.6. The Strong Markov Property and the Reflection Principle.- 2.7. Brownian Filtrations.- 2.8. Computations Based on Passage Times.- 2.9. The Brownian Sample Paths.- 2.10. Solutions to Selected Problems.- 2.11. Notes.- 3 Stochastic Integration.- 3.1. Introduction.- 3.2. Construction of the Stochastic Integral.- 3.3. The Change-of-Variable Formula.- 3.4. Representations of Continuous Martingales in Terms of Brownian Motion.- 3.5. The Girsanov Theorem.- 3.6. Local Time and a Generalized Itô Rule for Brownian Motion.- 3.7. Local Time for Continuous Semimartingales.- 3.8. Solutions to Selected Problems.- 3.9. Notes.- 4 Brownian Motion and Partial Differential Equations.- 4.1. Introduction.- 4.2. Harmonic Functions and the Dirichlet Problem.- 4.3. The One-Dimensional Heat Equation.- 4.4. The Formulas of Feynman and Kac.- 4.5. Solutions to selected problems.- 4.6. Notes.- 5 Stochastic Differential Equations.- 5.1. Introduction.- 5.2. Strong Solutions.- 5.3. Weak Solutions.- 5.4. The Martingale Problem of Stroock and Varadhan.- 5.5. A Study of the One-Dimensional Case.- 5.6. Linear Equations.- 5.7. Connections with Partial Differential Equations.- 5.8. Applications to Economics.- 5.9. Solutions to Selected Problems.- 5.10. Notes.- 6 P. Lévy's Theory of Brownian Local Time.-6.1. Introduction.- 6.2. Alternate Representations of Brownian Local Time.- 6.3. Two Independent Reflected Brownian Motions.- 6.4. Elastic Brownian Motion.- 6.5. An Application: Transition Probabilities of Brownian Motion with Two-Valued Drift.- 6.6. Solutions to Selected Problems.- 6.7. Notes.

SynopsisThis perennial best-seller is now in its fourth printing. Designed as a text for graduate courses in stochastic processes, it focuses on the hot topic of Brownian motion. The author is one of the leaders in the field of stochastics and finance. The text is complemented by a large number of problems and exercises., This book is designed as a text for graduate courses in stochastic processes. It 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 text is complemented by a large number of problems and exercises., This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish 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. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This 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 text is complemented by a large number of problems and exercises.

LC Classification NumberQA273.A1-274.9