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Parameter Estimation in Fractional Diffusion Models

Parameter Estimation in Fractional Diffusion Models

by Kestutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko

Publisher: Springer International Publishing
ISBN: 9783319710297
Pages: 390
Format: pdf, ePub, mobi, fb2
File size: 10 Mb
Date posting: 2020-11-20
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Parameter Estimation in Fractional Diffusion Models by Kestutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko 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.