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, and
it's also what makes this book such an important contribution to the
field. The purpose of the text here 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.