exponent_decay_of_fourier_fransform_of_brownian_motion
- To: mathgroup at smc.vnet.net
- Subject: [mg41806] exponent_decay_of_fourier_fransform_of_brownian_motion
- From: "Jose R. Campanha" <campanha at rc.unesp.br>
- Date: Fri, 6 Jun 2003 09:50:37 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Dear mathgroup
I'd like to find the value of the exponent decay of the fourier
transform of the brownian motion
(that I think is near 2), then I do
<<Statistics`ContinuousDistributions`
<<Graphics`Graphics`
ndist = NormalDistribution[0, 1]
RandomWalk[n_]:=Flatten[NestList[#+RandomArray[ndist,1]&,0,n]]
list1=RandomWalk[4096];
ListPlot[list1,PlotJoined->True]
list2=Chop[Abs[Fourier[list1]]];
LogListPlot[list2,PlotJoined=True,PlotRange=All]
list3=Drop[list2,-2049];
Length[list3]
len=Length[list3]
freq=0.5 Range[len]/len;
Length[freq]
power=list3;
endlist=Transpose[{freq,power}];
LogListPlot[endlist,PlotJoined=True,PlotRange=All];
Fit[Log[endlist],{1,x},x]
And the value was near 1.
Could someone help?
Jos=E9 R. Campanha
Physics Dpto
UNESP - Rio Claro