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## Details

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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