Stochastic Calculus for Fractional Brownian Motion and Related Processes

The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0

List of contents

Wiener Integration with Respect to Fractional Brownian Motion.- Stochastic Integration with Respect to fBm and Related Topics.- Stochastic Differential Equations Involving Fractional Brownian Motion.- Filtering in Systems with Fractional Brownian Noise.- Financial Applications of Fractional Brownian Motion.- Statistical Inference with Fractional Brownian Motion.

Summary

This volume examines the theory of fractional Brownian motion and other long-memory processes. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. It proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.

Product details

• Authors: Yuliya Mishura, Yuliya S. Mishura
• Assisted by: J.- M. Morel Cachan (Editor), F.Takens Groningen (Editor), B.Teissier Paris (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 14.04.2009
• EAN: 9783540758723
• ISBN: 978-3-540-75872-3
• No. of pages: 398
• Dimensions: 155 mm x 22 mm x 235 mm
• Weight: 646 g
• Illustrations: XVIII, 398 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Spieltheorie, Stochastik, B, Game Theory, Economics, Social and Behav. Sciences, Mathematics and Statistics, game theory, Probability Theory and Stochastic Processes, Probabilities, Stochastics, Probability Theory, stochastic integration