9781461495871
IR
EN-52530
انگلیسی
IR
Introduction to Stochastic Integratio
[Book]
/ electronic resource
2. ed. 2014.
New York, NY
: Springer New York :Imprint: Birkh?user,
, 2014.
XVII, 276 s. 10 illus. , online resource..
(Modern Birkh?user Classics,2197-1803)
9781461495864.
Electronic
Summary: 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. a Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then Ito@2019s change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman@2013Kac functional and theaSchr?dinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed. a New to the second edition are a discussion of the Cameron@2013Martin@2013Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use. a This book will be a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis. a 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 a a An attractive text@2026written in [a] lean and precise style@2026eminently readable. Especially pleasant are the care and attention devoted to details@2026 A very fine book. "Mathematical Reviews a.
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.
Modern Birkh?user Classics,2197-1803
Mathematics
Distribution (Probability theory)
Mathematics
Probability Theory and Stochastic Processes
E-BOOK
Chung, K.L..
Williams, R.J
SpringerLink (Online service)
ایران
9781461495864.pdf
عادی
عادی
9781461495864.pdf
متن
old catalog
e
BL
1
a
Y
