Jean-François Le Gall

Brownian Motion, Martingales, and Stochastic Calculus (eBook, PDF)

• Format: PDF

Produktbeschreibung

Provides a concise and rigorous presentation of stochastic integration and stochastic calculus for continuous semimartingales

Presents major applications of stochastic calculus to Brownian motion and related stochastic processes

Includes important aspects of Markov processes with applications to stochastic differential equations and to connections with partial differential equations

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Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 273
• Erscheinungstermin: 28. April 2016
• Englisch
• ISBN-13: 9783319310893
• Artikelnr.: 46927851

Autorenporträt

Jean-François 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 Université Paris-Sud and a member of the French Academy of Sciences.

Inhaltsangabe

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.

Rezensionen

"'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)