Brownian Motion, Martingales, and Stochastic Calculus (inbunden)
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Format
Inbunden (Hardback)
Språk
Franska
Antal sidor
273
Utgivningsdatum
2016-05-09
Upplaga
1st ed. 2016
Förlag
Springer International Publishing AG
Originalspråk
French
Illustratör/Fotograf
Bibliographie 4 schwarz-weiße und 1 farbige Abbildungen
Illustrationer
1 Illustrations, color; 4 Illustrations, black and white; XIII, 273 p. 5 illus., 1 illus. in color.
Dimensioner
234 x 156 x 18 mm
Vikt
581 g
Antal komponenter
1
Komponenter
1 Hardback
ISBN
9783319310886

Brownian Motion, Martingales, and Stochastic Calculus

av Jean-Franois Le Gall
Inbunden,  Franska, 2016-05-09
382
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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 Its formula, the optional stopping theorem and Girsanovs 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 It, 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 astrong 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.
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Fler böcker av Jean-Franois Le Gall

  • Measure Theory, Probability, and Stochastic Processes

    Measure Theory, Probability, and Stochastic Processes

    Jean-Franois Le Gall

    This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian m...

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Recensioner i media

The aim of this book is to provide a rigorous introduction to the theory of stochastic calculus for continuous semi-martingales putting a special emphasis on Brownian motion. If the reader has the background and needs a rigorous treatment of the subject this book would be a good choice. Le Gall writes clearly and gets to the point quickly . (Richard Durrett, MAA Reviews, March, 2017) The purpose of this book is to provide concise but rigorous introduction to the theory of stochastic calculus for continuous semimartingales, putting a special emphasis on Brownian motion. The book is written very clearly, it is interesting both for its construction and maintenance, mostly it is self-contained. It can be recommended to everybody who wants to study stochastic calculus, including those who is interested to its applications in other fields. (Yuliya S. Mishura, zbMATH, 2017)

Övrig information

Jean-Franois Le Gall is a well-known specialist of probability theory and stochastic processes. His main research achievements are concerned with Brownian motion, superprocesses and their connections with partial differential equations, and more recently random trees and random graphs. He has been awarded several international prizes in mathematics, including the Loeve Prize and the Fermat Prize, and gave a plenary lecture at the 2014 International Congress of Mathematicians. He is currently a professor of mathematics at Universit Paris-Sud and a member of the French Academy of Sciences.

Innehållsförteckning

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.

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