       Re: Differential Equation with Random Noise Input

• To: mathgroup at smc.vnet.net
• Subject: [mg49259] Re: Differential Equation with Random Noise Input
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Fri, 9 Jul 2004 02:26:43 -0400 (EDT)
• Organization: The University of Western Australia
• Sender: owner-wri-mathgroup at wolfram.com

```Lee Fisher <lfis at helix.nih.gov> wrote:

>I'm having trouble debugging this code.
>
> <<Statistics`NormalDistribution`
> <<Statistics`MultiDescriptiveStatistics`
> Res=1;
> Cap=.1;
> time=2;
> input[x_]:=Random[NormalDistribution[0,1]]
> listinput=Table[input[x/sample],{x,0,time*sample}]
> inputfun=Interpolation[listinput];
> result=NDSolve[{Res*Cap*V'[t]+V[t]==inputfun[t],V==0},V,{t,0,time}]
>
> This should be solving the differential equation using Gaussian white
> noise as the input, but I get the error:

As Jens pointed out, this is a stochatic differential equation. See e.g,

Gardiner, CW 1990 Handbook of Stochastic Methods
(2nd edn, Springer-Verlag, NY)

You can use Ito calculus on such problems. See e.g,

http://library.wolfram.com/infocenter/MathSource/1170/
http://www.mimuw.edu.pl/~akoz/Finance/SyllabusEng.html

Cheers,
Paul

--
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

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