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Theory of Martingales

Author: R Sh Liptser; A N Shiryayev
Publisher: Dordrecht : Springer Netherlands, 1989.
Series: Mathematics and Its Applications, Soviet Series, 49.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
One service mathematics has rc:ndered the 'Et moi, "', si j'avait su comment CD revenir, je n'y serais point alle. ' human race. It has put common SCIIJC back Jules Verne where it belongs. on the topmost shelf next to tbe dusty canister 1abdled 'discarded non- The series is divergent; tberefore we may be sense'. able to do sometbing witb it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: R Sh Liptser; A N Shiryayev
ISBN: 9789400924383 9400924380
OCLC Number: 851393827
Description: 1 online resource (812 pages).
Contents: I --
1. Basic Concepts and the Review of Results of {laquo}The General Theory of Stochastic Processes{raquo} --
2. Semimartingales. I. Stochastic Integral --
3. Random Measures and their Compensators --
4. Semimartingales. II Canonical Representation --
II --
5. Weak Convergence of Finite-Dimensional Distributions of Semimartingales to Distributions of Processes with Conditionally Independent Increments --
6. The Space D. Relative Compactness of Probability Distributions of Semimartingales --
7. Weak Convergence of Distributions of Semimartingales to Distributions of Processes with Conditionally Independent Increments --
8. Weak Convergence of Distributions of Semimartingales to the Distribution of a Semimartingale --
III --
9. Invariance Principle and Diffusion Approximation for Models Generated by Stationary Processes --
10. Diffusion Approximation for Semimartingales with a Normal Reflexion in a Convex Region --
Historic-Bibliographical notes.
Series Title: Mathematics and Its Applications, Soviet Series, 49.
Responsibility: by R. Sh. Liptser, A.N. Shiryayev.

Abstract:

One service mathematics has rc:ndered the 'Et moi, "', si j'avait su comment CD revenir, je n'y serais point alle. ' human race. It has put common SCIIJC back Jules Verne where it belongs. on the topmost shelf next to tbe dusty canister 1abdled 'discarded non- The series is divergent; tberefore we may be sense'. able to do sometbing witb it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science ... '; 'One service category theory has rendered mathematics ... '. All arguably true_ And all statements obtainable this way form part of the raison d'etre of this series_ This series, Mathematics and Its ApplicatiOns, started in 1977. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope_ At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches.

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