Algorithms for random fractals
The Science of Fractal Images
New methods for simulation of fractional Brownian motion
Journal of Computational Physics
SIAM Journal on Scientific Computing
Fast, approximate synthesis of fractional Gaussian noise for generating self-similar network traffic
ACM SIGCOMM Computer Communication Review
Fast simulation of overflow probabilities in a queue with Gaussian input
ACM Transactions on Modeling and Computer Simulation (TOMACS)
The design and evaluation of the Simple Self-Similar Sequences Generator
Information Sciences: an International Journal
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This article focuses on simulating fractional Brownian motion (fBm). Despite the availability of several exact simulation methods, attention has been paid to approximate simulation (i.e., the output is approximately fBm), particularly because of possible time savings. In this article, we study the class of approximate methods that are based on the spectral properties of fBm's stationary incremental process, usually called fractional Gaussian noise (fGn). The main contribution is a proof of asymptotical exactness (in a sense that is made precise) of these spectral methods. Moreover, we establish the connection between the spectral simulation approach and a widely used method, originally proposed by Paxson, that lacked a formal mathematical justification. The insights enable us to evaluate the Paxson method in more detail. It is also shown that spectral simulation is related to the fastest known exact method.