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MathGroup Archive 2002

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Re: Plot a sample path of a bornian motion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34974] Re: Plot a sample path of a bornian motion
  • From: wempenj at asme.org (JDW)
  • Date: Mon, 17 Jun 2002 03:26:48 -0400 (EDT)
  • References: <aeencs$9nh$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Kees" <keesvanschaik at wanadoo.nl> wrote in message news:<aeencs$9nh$1 at smc.vnet.net>...
> Hi,
> 
> I'm relatively new to Mathematica and am wondering how it's possible to plot
> a sample path of a (one-dimensional) Brownian motion. Any ideas?
> 
> Thanks in advance!

A couple of Do loops and the random function work.

1-D motion

num = 1000; (*number of points to plot*)
data = {};
newvalue = 0; (*initial strting position*)
Do[
   oldvalue = newvalue + Random[Real, {-1, 1}];
   data = Append[data, oldvalue];
   newvalue = oldvalue
 , {num}]
ListPlot[data, PlotJoined -> True]

2-D Motion

num = 1000;
datax = {};
datay = {};
newxvalue = 0;
newyvalue = 0;
Do[
   oldxvalue = newxvalue + Random[Real, {-1, 1}];
   datax = Append[datax, oldxvalue];
   newxvalue = oldxvalue;
   oldyvalue = newyvalue + Random[Real, {-1, 1}];
   datay = Append[datay, oldyvalue];
   newyvalue = oldyvalue
  , {num}]

dataxy = Transpose[{datax, datay}];
ListPlot[dataxy, PlotJoined -> True]

--JDW


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