Selected Aspects of Fractional Brownian Motion

• Main Author: Nourdin, Ivan (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Milano : Springer Milan : Imprint: Springer, 2012.
• Series: B&SS — Bocconi & Springer Series,
• Subjects: Mathematics.; Economics, Mathematical.; Probabilities.; Probability Theory and Stochastic Processes.; Quantitative Finance.

Fractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory pr...

Table of Contents:

• 1. Preliminaries
• 2. Fractional Brownian motion
• 3. Integration with respect to fractional Brownian motion
• 4. Supremum of the fractional Brownian motion
• 5. Malliavin calculus in a nutshell
• 6. Central limit theorem on the Wiener space
• 7. Weak convergence of partial sums of stationary sequences
• 8. Non-commutative fractional Brownian motion.