On the Long-Range Dependence of Fractional Brownian Motion

Ming Li

Mathematical Problems in Engineering, 2013, vol. 2013, 1-5

Abstract:

This paper clarifies that the fractional Brownian motion, , is of long-range dependence (LRD) for the Hurst parameter except . In addition, we note that the fractional Brownian motion is positively correlated for except . Moreover, we present a theorem to state that the differential or integral of a random function, , may substantially change the statistical dependence of . One example is that the differential of , in the domain of generalized functions, changes the LRD of to be of short-range dependence (SRD) when .

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:842197

DOI: 10.1155/2013/842197

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