Parameter Estimation In Fractional Diffusion Models (bocconi & Springer Series)
by Yuliya Mishura /
2018 / English / PDF
5 MB Download
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.
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.
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.