Sample Paths
Practical computer realisations of an fBm can be generated, although they are only a finite approximation. The sample paths chosen can be thought of as showing discrete sampled points on an fBm process. Three realisations are shown below, each with 1000 points of an fBm with Hurst parameter 0.75.
| H = 0.75 realisation 1 | H = 0.75 realisation 2 | H = 0.75 realisation 3 |
Two realisations are shown below, each showing 1000 points of an fBm, the first with Hurst parameter 0.95 and the second with Hurst parameter 0.55.
| H = 0.95 | H = 0.55 |
Read more about this topic: Fractional Brownian Motion
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Dare the unpastured dragon in his den?”
—Percy Bysshe Shelley (1792–1822)