Brownian motion, martingales, and stochastic calculus [electronic resource] / Jean-François Le Gall.
2016
QA274.75
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Details
Title
Brownian motion, martingales, and stochastic calculus [electronic resource] / Jean-François Le Gall.
ISBN
9783319310893 (electronic book)
3319310895 (electronic book)
9783319310886
3319310895 (electronic book)
9783319310886
Published
Switzerland : Springer, 2016.
Language
English
Description
1 online resource (xi, 273 pages) : illustrations.
Other Standard Identifiers
10.1007/978-3-319-31089-3 doi
Call Number
QA274.75
Dewey Decimal Classification
519.2/33
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed May 4, 2016).
Series
Graduate texts in mathematics ; 274.
Available in Other Form
Print version: 9783319310886
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Table of Contents
Gaussian variables and Gaussian processes
Brownian motion
Filtrations and martingales
Continuous semimartingales
Stochastic integration
General theory of Markov processes
Brownian motion and partial differential equations
Stochastic differential equations
Local times
The monotone class lemma
Discrete martingales
References.
Brownian motion
Filtrations and martingales
Continuous semimartingales
Stochastic integration
General theory of Markov processes
Brownian motion and partial differential equations
Stochastic differential equations
Local times
The monotone class lemma
Discrete martingales
References.