Stochastic Integrals (Advanced Lectures in Mathematics): An Introduction - Brossura

Weizsacker, Heinrich Von

 
9783528063108: Stochastic Integrals (Advanced Lectures in Mathematics): An Introduction
Brossura
ISBN 10: 3528063106 ISBN 13: 9783528063108
Casa editrice: Friedrich Vieweg & Sohn Verlagsgesellschaft mbH, 1990

Sinossi

This text introduces at a moderate speed and in a thorough way the basic concepts of the theory of stochastic integrals and Ito calculus for sem i­ martingales. There are many reasons to study this subject. We are fascinated by the contrast between general measure theoretic arguments and concrete probabilistic problems, and by the own flavour of a new differential calculus. For the beginner, a lot of work is necessary to go through this text in detail. As areward it should enable her or hirn to study more advanced literature and to become at ease with a couple of seemingly frightening concepts. Already in this introduction, many enjoyable and useful facets of stochastic analysis show up. We start out having a glance at several elementary predecessors of the stochastic integral and sketching some ideas behind the abstract theory of semimartingale integration. Having introduced martingales and local martingales in chapters 2 - 4, the stochastic integral is defined for locally uniform limits of elementary processes in chapter S. This corresponds to the Riemann integral in one-dimensional analysis and it suffices for the study of Brownian motion and diffusion processes in the later chapters 9 and 12.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Contenuti

1. Warming Up.- 2. Filtrations and Processes.- 3. Martingales.- 4. Localization and Approximation.- 5. The Stochastic Integral.- 6. Predictability.- 7. Semimartingales and Stochastic Differentials.- 8. Itô Calculus.- 9. The Special Role of Brownian Motion.- 10. Change of Measure.- 11. Stochastic Differential Equations.- 12. Towards Diffusions.- References.- Index of Common Notation.

Product Description

Book by Weizscker Heinrich von

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Editore
Friedrich Vieweg & Sohn Verlagsgesellschaft mbH
Data di pubblicazione
1990
Lingua
Inglese
ISBN 10 
3528063106
ISBN 13 
9783528063108
Rilegatura
Copertina flessibile
Numero di pagine
348
Contatto del produttore
ProductSafety@springernature.com
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Poststr. 9
Darmstadt
64293
Germania

Altre edizioni note dello stesso titolo

9783528163105: Stochastic Integrals: An Introduction

Edizione in evidenza

ISBN 10:  3528163100 ISBN 13:  9783528163105
Casa editrice: Friedrich Vieweg & Sohn Verl..., 1995
Brossura