Re: Fractal brownian motion?
From: G. A. Edgar (edgar_at_math.ohio-state.edu)
Date: 02/27/05
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Date: Sun, 27 Feb 2005 16:00:09 +0000 (UTC)
In article <cvr9j8$v16$1@news.ks.uiuc.edu>, Fred <farengeti@yahoo.com>
wrote:
> I'm a bit new to stochastic processes, so please forgive.
>
> I am interested in estimating the distribution of a variable R(t).
> The evolution of R(t) obeys the markov property.
> With probability 1/2, R(t) = F(R(t-1))
> With probability 1/2, R(t) = G(R(t-1))
> where F() and G() are two functions.
>
> Here F(R) = A + Mf *(R-A)
> and G(R) = B - Mg *(B-R)
>
> where A < B, and Mf,Mg < 1.
>
> Certainly this is not an example of normal Brownian motion, as the
> size of the step depends on the state of the system. The system
ends
> up bounded in (A,B), and at least for some values of the parameters
> the distribution of states seems to have a fractal structure.
>
> However, the discussions of fractal brownian motion, are usually
> formulated in terms of continuous processes,
Not just "usually" but "always" I think.
A discrete-time case, like this, is called "random walk" and not
"Brownian motion".
>
> and I can't seem to get
> my head around the Hurst parameter.
>
"Hurst parameter" is defined in certain situations, but not in others.
What is its definition?
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