This book is devoted to parameter estimation in diffusion models
involving fractional Brownian motion and related processes. For many
years now, standard Brownian motion has been (and still remains) a
popular model of randomness used to investigate processes in the natural
sciences, financial markets, and the economy. The substantial limitation
in the use of stochastic diffusion models with Brownian motion is due to
the fact that the motion has independent increments, and, therefore, the
random noise it generates is "white," i.e., uncorrelated. However, many
processes in the natural sciences, computer networks and financial
markets have long-term or short-term dependences, i.e., the correlations
of random noise in these processes are non-zero, and slowly or rapidly
decrease with time. In particular, models of financial markets
demonstrate various kinds of memory and usually this memory is modeled
by fractional Brownian diffusion. Therefore, the book constructs
diffusion models with memory and provides simple and suitable parameter
estimation methods in these models, making it a valuable resource for
all researchers in this field.
The book is addressed to specialists and researchers in the theory and
statistics of stochastic processes, practitioners who apply statistical
methods of parameter estimation, graduate and post-graduate students who
study mathematical modeling and statistics.
