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Title: Introduction to Stochastic Integration (Probability and Its Applications) by K.L. Chung, R.J. Williams ISBN: 0-8176-3386-3 Publisher: Birkhauser Boston Pub. Date: 01 October, 1990 Format: Hardcover Volumes: 1 List Price(USD): $59.95 |
Average Customer Rating: 5 (1 review)
Rating: 5
Summary: An excellent introduction to Stochastic Integration
Comment: 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!
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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Title: Stochastic Differential Equations: An Introduction With Applications (Universitext) by B. K. Ksendal, Bernt Ksendal, Bernt Oksendal ISBN: 3540047581 Publisher: Springer-Verlag Pub. Date: 01 December, 2003 List Price(USD): $44.95 |
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Title: A Probability Path by Sidney I. Resnick ISBN: 081764055X Publisher: Birkhauser Boston Pub. Date: 21 December, 1998 List Price(USD): $64.95 |
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Title: Limit Theorems for Stochastic Processes by J. Jacod, Albert Nikolaevich Shiriaev, Jean Jacod, N. Shiryaev ISBN: 3540439323 Publisher: Springer-Verlag Pub. Date: 16 December, 2002 List Price(USD): $153.00 |
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Title: Diffusions, Markov Processes, and Martingales: Foundations (Cambridge Mathematical Library) by L. C. G. Rogers, David Williams, D. Williams ISBN: 0521775949 Publisher: Cambridge University Press Pub. Date: 01 August, 2000 List Price(USD): $42.00 |
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Title: A Course in Probability Theory Revised by Kai Lai Chung ISBN: 0121741516 Publisher: Academic Press Pub. Date: 15 January, 2000 List Price(USD): $64.95 |
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