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MathGroup Archive 2004

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Re: f'[t]== x[t]+u[t] ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51612] Re: f'[t]== x[t]+u[t] ?
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 27 Oct 2004 01:54:28 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <clcnpn$q4m$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

you have to derive a Fokker-Planck equation from your stochastic ode
and solve this one and you need some assumptions about the character
of the noise (white noise ?)
Regards
  Jens

"ames kin" <ames_kin at yahoo.com> schrieb im Newsbeitrag 
news:clcnpn$q4m$1 at smc.vnet.net...
>I was thinking about solving that using Mathematica. Clearly I do not have
> enough math background. I wanted to get some feedbacks from the group.
>
> let,
>
> f'[t]== x[t]+u[t] where u[t] is the noise term. or fluctuation term.
>
> When you have a system with noise present, ( as in stochastic ode) is
> it Ok or acceptable to obtain the deterministic solution in the form
> of Mathematica InterpolatingFunction, and then add the noise when you 
> Evaluate
> the InterpolatingFunction.
>
> ie,
>
> << Graphics`Colors`
> << Graphics`Graphics`
>
> sol = NDSolve[{Derivative[3][y][x] + Derivative[2][y][x] +
> Derivative[1][y][x] == -y[x]^3, y[0] == 1, Derivative[1][y][0] ==
> Derivative[2][y][0] == 0}, y, {x, 0, 20}];
>
> which outputs an interpolating function which has to be "evaluated"
> before it can be plotted.  If so, If I throw in fluctuation as one
> Table the evaluation, it will have an appearance of wide fluctuation.
>
> so,
>
> Table[Evaluate[y[x] /. sol[[1]]] + Random[Real, {-0.3, 0.3}], {x, 0,
> 20, 0.2}]
>
> which then can be plotted.
>
> ListPlot[Table[Evaluate[y[x] /. sol[[1]]] + Random[Real, {-0.3,
> 0.3}], {x, 0, 20, 0.2}], PlotStyle -> {GrayLevel[0.8]},  PlotJoined ->
> True, PlotRange -> All, Axes -> False, Frame -> True, DisplayFunction
> -> Identity];
>
> What is wrong with this method of solution for a system such as
> f'[t] == x[t] + u[t] ? (where u is the noise. this is my, most likely
> erroneous, interpretation of stochastic ode)
>
> I mean, what is wrong with this method mathematically.
>
> thanks in advance for any feedback from the group.
> 



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