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Field name	Details
Dewey Class	519.2
Title	Introduction to Stochastic Integration (EB) / by K.L. Chung, R.J. Williams.
Author	Chung, Kai Lai , 1917-2009
Added Personal Name	Williams, R.J.
Other name(s)	SpringerLink (Online service)
Edition statement	2nd ed. 2014.
Publication	New York, NY Birkhäuser 2014.
Physical Details	XVII, 276 pages: 10 illus. : online resource.
ISBN	9781461495871
Summary Note	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 Itô’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 will be 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 :
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4614-9587-1
Links to Related Works	Subject References: Distribution (Probability theory) . Mathematics . Probability theory and stochastic processes . Authors: author . Chung, Kai Lai 1917-2009 . Chung, Kai Lai, 1917-2009. . Williams, R.J. . Corporate Authors: SpringerLink (Online service) . Series: Modern Birkhäuser classics . Classification: 519.2 .

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Introduction to Stochastic Integration

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