Brownian Motion, Martingales, and Stochast...

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Beschreibung

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 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.

Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2016
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Graduate Texts in Mathematics
Inhalt:	xiii 273 S. 4 s/w Illustr. 1 farbige Illustr. 273 p. 5 illus. 1 illus. in color.
ISBN-13:	9783319310886
ISBN-10:	3319310887
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Le Gall, Jean-François
Auflage:	1st ed. 2016
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG Graduate Texts in Mathematics
Maße:	241 x 160 x 22 mm
Von/Mit:	Jean-François Le Gall
Erscheinungsdatum:	09.05.2016
Gewicht:	0,6 kg

Artikel-ID: 103980984