Biagini / Hu / Øksendal Stochastic Calculus for Fractional Brownian Motion and Applications

1. Auflage 2008
ISBN: 978-1-84628-797-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 330 Seiten, eBook

Reihe: Probability and Its Applications

Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This huge range of potential applications makes fBm an interesting object of study. Several approaches have been used to develop the concept of stochastic calculus for fBm. The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. Particular emphasis is placed on studying the relations between the different approaches. Readers are assumed to be familiar with probability theory and stochastic analysis, although the mathematical techniques used in the book are thoroughly exposed and some of the necessary prerequisites, such as classical white noise theory and fractional calculus, are recalled in the appendices. This book will be a valuable reference for graduate students and researchers in mathematics, biology, meteorology, physics, engineering and finance.

Zielgruppe

Research

Autoren/Hrsg.

Biagini, Francesca

Hu, Yaozhong

Øksendal, Bernt

Zhang, Tusheng

Inhaltsverzeichnis

Fractional Brownian motion.- Intrinsic properties of the fractional Brownian motion.- Stochastic calculus.- Wiener and divergence-type integrals for fractional Brownian motion.- Fractional Wick Itô Skorohod (fWIS) integrals for fBm of Hurst index H >1/2.- WickItô Skorohod (WIS) integrals for fractional Brownian motion.- Pathwise integrals for fractional Brownian motion.- A useful summary.- Applications of stochastic calculus.- Fractional Brownian motion in finance.- Stochastic partial differential equations driven by fractional Brownian fields.- Stochastic optimal control and applications.- Local time for fractional Brownian motion.