Beschreibung
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.
Inhaltsverzeichnis
Part I: Fractional Brownian Motion.- Intrinsic properties of the fractional Brownian motion. Part II: Stochastic Calculus.- Wiener and divergence-type integrals for fractional Brownian motion.- Fractional Wick-Ito-Skorohod (fWIS-) integrals for fractional Brownian motion of Hurst Index H > ½.- Wick-Ito-Skorohod integrals for fractional Brownian motion.- Pathwise integrals for fractional Brownian motion.- A useful summary. Part III: 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. Part IV: Appendices.- Classical Malliavin calculus.- Notions from fractional calculus.- Estimation of Hurst parameter.- Stochastic differential equations for fBm.- References.- List of symbols and notation.- Index.
