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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





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