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" Theory of Martingales "
by R. Sh. Liptser, A.N. Shiryayev.
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BL
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| Record Number
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772871
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b592865
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| Main Entry
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by R. Sh. Liptser, A.N. Shiryayev.
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| Title & Author
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Theory of Martingales\ by R. Sh. Liptser, A.N. Shiryayev.
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| Publication Statement
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Dordrecht : Springer Netherlands, 1989
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| Series Statement
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Mathematics and Its Applications, Soviet Series, 49.
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(812 pages)
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| ISBN
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9400924380
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: 9789400924383
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| Contents
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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.
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| Abstract
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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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Computer engineering.
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Statistics.
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| LC Classification
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QA274.5B977 1989
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A N Shiryayev
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R Sh Liptser
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