Stochastic Integrals

An Introduction

Heinrich von Weizsäcker (Autor)

Buch | Softcover

IX, 332 Seiten

1990 | 1990
Vieweg & Teubner (Verlag)
978-3-528-06310-8 (ISBN)

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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.

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.

Erscheint lt. Verlag	1.1.1990
Reihe/Serie	Advanced Lectures in Mathematics
Zusatzinfo	IX, 332 S. 5 Abb.
Verlagsort	Wiesbaden
Sprache	deutsch
Maße	155 x 235 mm
Gewicht	476 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Approximation • Brownian motion • Differentialgleichung • Filtration • Gleichung • Integralrechnung • Martingal • Martingale • Semimartingal • semimartingale • Stochastik • Stochastische Differentialgleichung
ISBN-10	3-528-06310-6 / 3528063106
ISBN-13	978-3-528-06310-8 / 9783528063108
Zustand	Neuware