On spectral simulation of fractional Brownian motion
نویسنده
چکیده
This paper 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 paper, 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. 2000 Mathematics Subject Classification: 65C05, 62M15
منابع مشابه
Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
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