Fractional Brownian motion (f Bm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This huge range of potential applications makes f Bm an interesting object of study. Several approaches have been used to develop the concept of stochastic calculus for f Bm. The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for f Bm, 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.
Tabela de Conteúdo
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 (f WIS) integrals for f Bm of Hurst index H >1/2.- Wick Itô 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.
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