Description
Springer Stochastic Calculus For Fractional Brownian Motion And Applications 2010 Edition by Francesca Biagini Yaozhong Hu Bernt Öksendal Tusheng Zhang
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. Table of contents : Fractional Brownian motion.- Intrinsic properties of the fractional Brownian motion.- Stochastic calculus.- Wiener and divergence-type integrals for fractional Brownian motion.- Fractional Wick Ito Skorohod (fWIS) integrals for fBm of Hurst index H >1/2.- WickIto 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.