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Re: White Noise in Simulation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg103674] Re: White Noise in Simulation
  • From: SlipperyWeasel <slipperyweasel at gmail.com>
  • Date: Fri, 2 Oct 2009 08:22:41 -0400 (EDT)
  • References: <h9p69i$vu$1@smc.vnet.net> <200909291136.HAA25463@smc.vnet.net>

On Sep 30, 5:04 am, DrMajorBob <btre... at austin.rr.com> wrote:
> v can't be both continuous AND white noise. The best you can do (I think)=
  
> is something like this:
>
> sigma = 3.5;
> {start, stop} = {-Pi, Pi};
> n = 20;
> v = Interpolation@
>     Table[{t, RandomReal@NormalDistribution[0, sigma]}, {t, start,
>       stop, (stop - start)/(n - 1)}];
> Clear[x]
> x = x /. First@
>      NDSolve[{x'[t] == x[t] + Sin[t] + v[t], x[start] == 0}=
,
>       x, {t, start, stop}];
> Plot[{v@t, x@t}, {t, start, stop}]
>
> Run that code several times, and you'll see very different results.
>
> If sigma is small, though, v will hardly matter at all.
>
> Bobby
>
> On Tue, 29 Sep 2009 06:36:17 -0500, SlipperyWeasel  
>
> <slipperywea... at gmail.com> wrote:
> > On Sep 27, 10:16 pm, SlipperyWeasel <slipperywea... at gmail.com> wrote:
> >> I am trying to add random noise to a function inside an NDSolve
> >> function.  Is there a good way to add a "noise function" in my model=
?
>
> > for example, my system is:  x'[t] == x[t] + Sin[t] + v
> > where v is Gaussian white noise.
>
> > v has to be a continuous function of t in order to use NDSolve on the
> > ODE, but it also should be uncorrelated.  How can I make this a
> > continuous function while still making it uncorrelated?
>
> --
> DrMajor... at yahoo.com

Thanks for the suggestions so far.  I had been basically interpolating
a random distribution before as most of you suggested.  I now have
switched to using the Kac-Shinozuka white noise, which gives me hte
same results but is quicker and actually continuous.


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