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
Famous quotes containing the words sample and/or paths:
“All that a city will ever allow you is an angle on it—an oblique, indirect sample of what it contains, or what passes through it; a point of view.”
—Peter Conrad (b. 1948)
“Now the hungry lion roars,
And the wolf behowls the moon;
Whilst the heavy ploughman snores,
All with weary task fordone.
Now the wasted brands do glow,
Whilst the screech-owl, screeching loud,
Puts the wretch that lies in woe
In remembrance of a shroud.
Now it is the time of night,
That the graves, all gaping wide,
Every one lets forth his sprite,
In the church-way paths to glide:”
—William Shakespeare (1564–1616)