Simulation of fractional Brownian motion
نویسنده
چکیده
Preface In recent years, there has been great interest in the simulation of long-range dependent processes, in particular fractional Brownian motion. Motivated by applications in communications engineering, I wrote my master's thesis on the subject in 2002. Since many people turned out to be interested in various aspects of fractional Brownian motion, I decided to update my thesis and make it publicly available. Some references are added and the section on spectral simulation is rewritten according to the paper [22]. Fractional Brownian motion is not only of interest for communications engineers. Its properties have been investigated by researchers in theoretical physics, probability, statistics, hydrology, biology, and many others. As a result, the techniques that have been used to study this Gaussian process are quite diverse, and it may take some effort to study them. Undoubtedly, this also makes the field more interesting. This report gives an introduction to generation and estimation of fractional Brownian motion. However, as the literature on the subject is quite extensive (see, for instance, [24]), it has not been my goal to write a complete introduction. Running the risk of satisfying nobody, it is my hope that this report provides some help to find a way through the literature. Since it is written on the level of a master's student, limited background is required. I would like to take this opportunity to thank my thesis advisor, Michel Mandjes, for many discussions and for his help to prepare this manuscript. Finally, I refer to my homepage http://www.cwi.nl/~ton for the C code that was used to write this report. Amsterdam, February 2004 Ton Dieker It is my great pleasure to thank Antoine Ayache for valuable discussions on wavelet methods for simulating fractional Brownian motion. He pointed me out that the section on wavelets contained a serious error, which led me to revise it.
منابع مشابه
Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
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تاریخ انتشار 2004