- Paperback: 191 pages
- Publisher: Birkhauser (Jun 1983)
- Language: English
- ISBN-10: 0817631178
- ISBN-13: 978-0817631178
- Product Dimensions: 23.1 x 15 x 1.8 cm
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Introduction to Stochastic Integration
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"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
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First Sentence
For each interval I in IR = (-oo, oo) let B(I) denote the o-field of Borel subsets of I. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
For each interval I in IR = (-oo, oo) let B(I) denote the o-field of Borel subsets of I. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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31 of 32 people found the following review helpful
5.0 out of 5 stars
An excellent introduction to Stochastic Integration
27 Feb 2002
By Alan Bain
- Published on Amazon.com
Format:Hardcover
This book provides a very easy to read account of the development of the stochastic integral. While concentrating on integrators which are continuous local martingales, and thus lacking the full generality of treatment to be found in, for example Dellacherie
and Meyer, the basic constructions are all performed in a fashion which is readily extensible to the more general case. From a teaching point of view this is beneficial if the more general case is to be studied subsequently. Although the arguments can be considerably simplified for specific special cases (e.g. integration with respect to Brownian Motion only), it is useful to understand how the construction fits into the more general case, which also makes less of a discontinuity for the reader who is subsequently to study the general discontinuous theory!
and Meyer, the basic constructions are all performed in a fashion which is readily extensible to the more general case. From a teaching point of view this is beneficial if the more general case is to be studied subsequently. Although the arguments can be considerably simplified for specific special cases (e.g. integration with respect to Brownian Motion only), it is useful to understand how the construction fits into the more general case, which also makes less of a discontinuity for the reader who is subsequently to study the general discontinuous theory!
The arguments are presented carefuly, for example all of the necesary conditions being checked explicitly in places where important theorems are to be applied, and there are none of the annoying statements which plague books on Stochastic Calculus along the lines "the reader can readily check", or "see problem 21.2.43" in the middle of proofs. Additionally very few lines are "skipped" in the proofs; while this does mean that they are lacking in brevity, it is strongly to be encouraged when a complex subject is presented to the novice. When the concepts are understood sufficiently well the reader can easily compile "brief" proofs on his own (as a form of revision), but working the other way round frequently, in my experience of supervising a similar course, leads to misapprehensions about the conditions for applying essential theorems.
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