Introduction to Stochastic Integration

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Beschreibung

A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability.
Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then It¿s change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman¿Kac functional and the Schrödinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed.
New to the second edition are a discussion of the Cameron¿Martin¿Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use.
This book willbe a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis.
The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory.
¿Journal of the American Statistical Association
An attractive text¿written in [a] lean and precise style¿eminently readable. Especially pleasant are the care and attention devoted to details¿ A very fine book.
¿Mathematical Reviews

Über den Autor

Professor Chung and Professor Williams

Zusammenfassung

Affordable, softcover reprint of a classic textbook

Authors' exposition consistently chooses clarity over brevity

Includes an expanded collection of exercises from the first edition

Includes supplementary material: [...]

Inhaltsverzeichnis

1 Preliminaries.- 2 Definition of the Stochastic Integral.- 3 Extension of the Predictable Integrands.- 4 Quadratic Variation Process.- 5 The Ito Formula.- 6 Applications of the Ito Formula.- 7 Local Time and Tanaka's Formula.- 8 Reflected Brownian Motions.- 9 Generalization Ito Formula, Change of Time and Measure.- 10 Stochastic Differential Equations.- References.- Index.

Details

Erscheinungsjahr:	2013
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	296
Reihe:	Modern Birkhäuser Classics
Inhalt:	xvii 276 S. 10 s/w Illustr. 276 p. 10 illus.
ISBN-13:	9781461495864
ISBN-10:	1461495865
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Williams, R. J. Chung, K. L.
Auflage:	2nd ed. 2014
Hersteller:	Springer US Springer New York Modern Birkhäuser Classics
Maße:	235 x 155 x 17 mm
Von/Mit:	R. J. Williams (u. a.)
Erscheinungsdatum:	10.11.2013
Gewicht:	0,452 kg

preigu-id: 105616412