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]==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://math.uc.edu/~srdjan/AD.pdf
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
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