R. Liptser, A. N. Shiryayev

Theory of Martingales

• Gebundenes Buch

Produktbeschreibung

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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Produktdetails

• Mathematics and Its Applications 49
• Verlag: Springer / Springer Netherlands
• Artikelnr. des Verlages: 978-0-7923-0395-4
• 1989.
• Seitenzahl: 812
• Erscheinungstermin: 30. September 1989
• Englisch
• Abmessung: 241mm x 160mm x 49mm
• Gewicht: 1306g
• ISBN-13: 9780792303954
• ISBN-10: 0792303954
• Artikelnr.: 21042371

Inhaltsangabe

I.- 1. Basic Concepts and the Review of Results of «The General Theory of Stochastic Processes».- 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.