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?
>

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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