Stochastic Analysis in Discrete and Continuous Settings

With Normal Martingales
1. Auflage 2009
ISBN: 978-3-642-02379-8
Verlag: Springer

Buch, Englisch, Band 1982, 282 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1020 g

Reihe: Lecture Notes in Mathematics

This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.

Zielgruppe

Research

Autoren/Hrsg.

Privault, Nicolas

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Finanz- und Versicherungsmathematik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

The Discrete Time Case.- Continuous Time Normal Martingales.- Gradient and Divergence Operators.- Annihilation and Creation Operators.- Analysis on the Wiener Space.- Analysis on the Poisson Space.- Local Gradients on the Poisson Space.- Option Hedging in Continuous Time.