عنوان

Theory of Martingales

(Number (ISBN

9400924380

(Number (ISBN

9789400924383

Number

b592865

Title Proper

Theory of Martingales

General Material Designation

[Book]

First Statement of Responsibility

by R. Sh. Liptser, A.N. Shiryayev.

Place of Publication, Distribution, etc.

Dordrecht

Name of Publisher, Distributor, etc.

Springer Netherlands

Date of Publication, Distribution, etc.

1989

Specific Material Designation and Extent of Item

(812 pages)

Series Title

Mathematics and Its Applications, Soviet Series, 49.

Text of Note

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.

Text of Note

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.

Computer engineering.

Statistics.

Class number

Book number

by R. Sh. Liptser, A.N. Shiryayev.

A N Shiryayev

R Sh Liptser

Electronic name

[Book]

Y