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But here the word "representation" is being used in a different way that I don't understand, referring to the assertion that the representation is "4-dimensional" and has a given "basis" These words suggest that some vector space is being considered here.
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305:
Does anyone happen to know what the fractal dimension of this function is? It's not listed anywhere on the
Internet, but a quick box-counting estimate gives 1.03037, which suggests it could well actually be 1, at least for w=1/2.
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285:
I don't think that Hurst parameter should redirect to this page. I was going to add a link from the page on fractional
Brownian motion, but this page is no more about the Hurst parameter than that page is.
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I reduced the section "differentiability", that contained wrong and unclear statements. However it may be expanded again hopefully. A more complete exposition should give the modulus of continuity of
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Previously that article was discussing "representations" of the
Blancmange curve or its integral via various infinite series.
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This integral is also self-similar on the unit interval, under an action of the dyadic monoid described in the section
846:. It is "commuting" in that the order of R and g are exchanged with one-another. In this representation, each element
1307:. This is just a linear equation. Does this answer your question? I will try to edit the article to clarify this.
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in that n-dimensional space. In this article, its not actually a group, but a monoid, but the same ideas apply.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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629:{\displaystyle (x)=I_{w}\left({\frac {x}{2}}\right)={\frac {x^{2}}{8}}+{\frac {w}{2}}I_{w}(x)}
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1112:. That is, given ANY 4-D vector (a,b,c,d) one has the corresponding vector representation
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much, much, much clearer explanation of what "dimension" and "basis" are about would be
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on the interval ). Also, a more precise statement about the differentiability for
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1/2 ( Hölder, I guess) and if possible, the exact value of the total variation of
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of "things" having some symmetry, one generally identifies that symmetry as a
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1105:{\displaystyle \{e_{1},e_{2},e_{3},e_{4}\}\mapsto \{1,x,x^{2},I(x)\}}
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A basis for an n-dimensional vector space is commonly written as
437:. Here, the representation is 4-dimensional, having the basis
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Would someone like to write a real Hurst parameter page?
1300:{\displaystyle g:(a,b,c,d)\mapsto (a,b/2,c/4+d/8,wd/2)}
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650:what vector space is being referred to
1175:{\displaystyle a+bx+cx^{2}+dI_{w}(x)}
665:2601:200:C000:1A0:211A:BDC0:4259:59DA
402:, by Marek Jarnicki and Peter Pflug.
7:
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262:This article is within the field of
200:This article is within the scope of
95:This article is within the scope of
747:and a collection of n x n matrices
38:It is of interest to the following
987:{\displaystyle \{1,x,x^{2},I(x)\}}
751:such that, for each group element
490:{\displaystyle \{1,x,x^{2},I(x)\}}
14:
1337:Low-priority mathematics articles
1182:and this vector transforms under
115:Knowledge:WikiProject Mathematics
1352:Systems articles in chaos theory
1332:Start-Class mathematics articles
424:Integrating the Blancmange curve
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118:Template:WikiProject Mathematics
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1347:Low-importance Systems articles
839:{\displaystyle R(gx)=M_{g}R(x)}
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725:{\displaystyle g:x\mapsto gx}
393:16:28, 28 December 2018 (UTC)
311:13:25, 10 February 2007 (UTC)
220:Knowledge:WikiProject Systems
109:and see a list of open tasks.
1357:WikiProject Systems articles
1342:Start-Class Systems articles
412:09:58, 18 January 2019 (UTC)
223:Template:WikiProject Systems
854:corresponds to some vector
648:, it it necessary to state
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673:14:28, 12 July 2022 (UTC)
296:23:34, 19 June 2006 (UTC)
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
